المؤلفون: Mizuta, Yoshihiro, Shimomura, Tetsu

مصطلحات موضوعية: keyword:variable exponent, keyword:fractional maximal function, keyword:Riesz potential, keyword:Sobolev's inequality, keyword:weighted Morrey space, keyword:double phase functional, msc:31B15, msc:42B25, msc:46E30

وصف الملف: application/pdf

Relation: reference:[1] Adams, D. R.: A note on Riesz potentials.Duke Math. J. 42 (1975), 765-778. Zbl 0336.46038, MR 0458158, 10.1215/S0012-7094-75-04265-9; reference:[2] Adams, D. R., Hedberg, L. I.: Function Spaces and Potential Theory.Grundlehren der Mathematischen Wissenschaften 314. Springer, Berlin (1995). Zbl 0834.46021, MR 1411441, 10.1007/978-3-662-03282-4; reference:[3] Almeida, A., Hasanov, J., Samko, S.: Maximal and potential operators in variable exponent Morrey spaces.Georgian Math. J. 15 (2008), 195-208. Zbl 1263.42002, MR 2428465, 10.1515/GMJ.2008.195; reference:[4] Baroni, P., Colombo, M., Mingione, G.: Non-autonomous functionals, borderline cases and related function classes.St. Petersbg. Math. J. 27 (2016), 347-379. Zbl 1335.49057, MR 3570955, 10.1090/spmj/1392; reference:[5] Baroni, P., Colombo, M., Mingione, G.: Regularity for general functionals with double phase.Calc. Var. Partial Differ. Equ. 57 (2018), Article ID 62, 48 pages. 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الاتاحة: http://hdl.handle.net/10338.dmlcz/151955

المؤلفون: Akdim, Youssef, Belayachi, Mohammed, Hjiaj, Hassane

مصطلحات موضوعية: keyword:renormalized solution, keyword:nonlinear elliptic equation, keyword:non-coercive problem, msc:35J60, msc:46E30, msc:46E35

وصف الملف: application/pdf

Relation: mr:MR4585581; zbl:Zbl 07729577; reference:[1] Alvino, A., Boccardo, L., Ferone, V., Orsina, L., Trombetti, G.: Existence results for nonlinear elliptic equations with degenerate coercivity.Ann. Mat. Pura Appl., IV. Ser. 182 (2003), 53-79. Zbl 1105.35040, MR 1970464, 10.1007/s10231-002-0056-y; reference:[2] Alvino, A., Ferone, V., Trombetti, G.: A priori estimates for a class of nonuniformly elliptic equations.Atti Semin. Mat. Fis. Univ. Modena 46 (1998), 381-391. Zbl 0911.35025, MR 1645729; reference:[3] Ali, M. Ben Cheikh, Guibé, O.: Nonlinear and non-coercive elliptic problems with integrable data.Adv. Math. Sci. Appl. 16 (2006), 275-297. Zbl 1215.35066, MR 2253236; reference:[4] Bénilan, P., Boccardo, L., Gallouët, T., Gariepy, R., Pierre, M., Vazquez, J. L.: An $L^1$-theory of existence and uniqueness of solutions of nonlinear elliptic equations.Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 22 (1995), 241-273. Zbl 0866.35037, MR 1354907; reference:[5] Bensoussan, A., Boccardo, L., Murat, F.: On a nonlinear partial differential equation having natural growth terms and unbounded solution.Ann. Inst. Henri Poincaré, Anal. Non Linéaire 5 (1988), 347-364. Zbl 0696.35042, MR 0963104, 10.1016/S0294-1449(16)30342-0; reference:[6] Blanchard, D., Guibé, O.: Infinite valued solutions of non-uniformly elliptic problems.Anal. Appl., Singap. 2 (2004), 227-246. Zbl 1129.35370, MR 2070448, 10.1142/S0219530504000369; reference:[7] Boccardo, L., Dall'Aglio, A., Orsina, L.: Existence and regularity results for some elliptic equations with degenerate coercivity.Atti Semin. Mat. Fis. Univ. Modena 46 (1998), 51-81. Zbl 0911.35049, MR 1645710; reference:[8] Boccardo, L., Gallouet, T.: Strongly nonlinear elliptic equations having natural growth terms and $L^1$ data.Nonlinear Anal., Theory Methods Appl. 19 (1992), 573-579. Zbl 0795.35031, MR 1183664, 10.1016/0362-546X(92)90022-7; reference:[9] Croce, G.: The regularizing effects of some lower order terms in an elliptic equation with degenerate coercivity.Rend. Mat. Appl., VII. Ser. 27 (2007), 299-314. Zbl 1147.35043, MR 2398428; reference:[10] Vecchio, T. Del, Posteraro, M. R.: Existence and regularity results for nonlinear elliptic equations with measure data.Adv. Differ. Equ. 1 (1996), 899-917. Zbl 0856.35044, MR 1392010; reference:[11] Pietra, F. Della: Existence results for non-uniformly elliptic equations with general growth in the gradient.Differ. Integral Equ. 21 (2008), 821-836. Zbl 1224.35117, MR 2483336; reference:[12] Droniou, J.: Non-coercive linear elliptic problems.Potential Anal. 17 (2002), 181-203. Zbl 1161.35362, MR 1908676, 10.1023/A:1015709329011; reference:[13] Droniou, J.: Global and local estimates for nonlinear noncoercive elliptic equations with measure data.Commun. Partial Differ. Equations 28 (2003), 129-153. Zbl 1094.35046, MR 1974452, 10.1081/PDE-120019377; reference:[14] Guibé, O., Mercaldo, A.: Existence and stability results for renormalized solutions to noncoercive nonlinear elliptic equations with measure data.Potential Anal. 25 (2006), 223-258. Zbl 1198.35072, MR 2255346, 10.1007/s11118-006-9011-7; reference:[15] Guibé, O., Mercaldo, A.: Existence of renormalized solutions to nonlinear elliptic equations with two lower order terms and measure data.Trans. Am. Math. Soc. 360 (2008), 643-669. Zbl 1156.35042, MR 2346466, 10.1090/S0002-9947-07-04139-6; reference:[16] Leone, C., Porretta, A.: Entropy solutions for nonlinear elliptic equations in $L^1$.Nonlinear Anal., Theory Methods Appl. 32 (1998), 325-334. Zbl 1155.35352, MR 1610574, 10.1016/S0362-546X(96)00323-9; reference:[17] Lions, J. L.: Quelques méthodes de résolution des problèmes aux limites non linéaires.Etudes mathematiques. Dunod, Gauthier-Villars, Paris (1969), French. Zbl 0189.40603, MR 0259693; reference:[18] Maderna, C., Pagani, C. D., Salsa, S.: Quasilinear elliptic equations with quadratic growth in the gradient.J. Differ. Equations 97 (1992), 54-70. Zbl 0785.35039, MR 1161311, 10.1016/0022-0396(92)90083-Y; reference:[19] Murat, F.: Soluciones renormalizadas de EDP elipticas non lineales.Technical Report R93023, Laboratoire d'Analyse Numérique, Paris (1993), French.; reference:[20] Porretta, A.: Nonlinear equations with natural growth terms and measure data.Electron. J. Differ. Equ. Conf. 09 (2002), 183-202. Zbl 1109.35341, MR 1976695; reference:[21] León, S. Segura de: Existence and uniqueness for $L^1$ data of some elliptic equations with natural growth.Adv. Differ. Equ. 8 (2003), 1377-1408. Zbl 1158.35365, MR 2016651; reference:[22] Trombetti, C.: Non-uniformly elliptic equations with natural growth in the gradient.Potential Anal. 18 (2003), 391-404. Zbl 1040.35010, MR 1953268, 10.1023/A:1021884903872; reference:[23] Zou, W.: Existence of solutions for a class of porous medium type equations with a lower order terms.J. Inequal. Appl. 2015 (2015), Article ID 294, 23 pages. Zbl 1336.35167, MR 3399257, 10.1186/s13660-015-0799-9

الاتاحة: http://hdl.handle.net/10338.dmlcz/151689

المؤلفون: Ohno, Takao, Shimomura, Tetsu

مصطلحات موضوعية: keyword:Riesz potential, keyword:Sobolev's inequality, keyword:Orlicz-Morrey space, keyword:metric measure space, keyword:non-doubling measure, msc:46E30, msc:46E35

وصف الملف: application/pdf

Relation: mr:MR4541101; zbl:Zbl 07655767; reference:[1] Adams, D. R.: A note on Riesz potentials.Duke Math. J. 42 (1975), 765-778. Zbl 0336.46038, MR 458158, 10.1215/S0012-7094-75-04265-9; reference:[2] Björn, A., Björn, J.: Nonlinear Potential Theory on Metric Spaces.EMS Tracts in Mathematics 17. European Mathematical Society, Zürich (2011). Zbl 1231.31001, MR 2867756, 10.4171/099; reference:[3] Burenkov, V. I., Guliyev, H. V.: Necessary and sufficient conditions for boundedness of the maximal operator in local Morrey-type spaces.Stud. Math. 163 (2004), 157-176. Zbl 1044.42015, MR 2047377, 10.4064/sm163-2-4; reference:[4] Cruz-Uribe, D. V., Shukla, P.: The boundedness of fractional maximal operators on variable Lebesgue spaces over spaces of homogeneous type.Stud. Math. 242 (2018), 109-139. Zbl 1397.42009, MR 3778907, 10.4064/sm8556-6-2017; reference:[5] Hajłasz, P., Koskela, P.: Sobolev met Poincaré.Mem. Am. Math. Soc. 688 (2000), 101 pages. 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الاتاحة: http://hdl.handle.net/10338.dmlcz/151516

المؤلفون: Tabatabaie, Seyyed Mohammad, Bagheri Salec, Alireza

مصطلحات موضوعية: keyword:Young function, keyword:Orlicz space, keyword:quasi-Banach function space, keyword:inclusion, msc:46E30

وصف الملف: application/pdf

Relation: mr:MR4536310; zbl:Zbl 07655813; reference:[1] Campo, R. del, Fernández, A., Mayoral, F., Naranjo, F.: Orlicz spaces associated to a quasi-Banach function space: Applications to vector measures and interpolation.Collect. Math. 72 (2021), 481-499. Zbl 07401995, MR 4297141, 10.1007/s13348-020-00295-1; reference:[2] Rao, M. M., Ren, Z. D.: Theory of Orlicz Spaces.Pure and Applied Mathematics 146. Marcel Dekker, New York (1991). Zbl 0724.46032, MR 1113700; reference:[3] Romero, J. L.: When is $L^p(\mu)$ contained in $L^q(\mu)$?.Am. Math. Mon. 90 (1983), 203-206. Zbl 0549.46018, MR 0691371, 10.2307/2975553; reference:[4] Sawano, Y., Tabatabaie, S. M.: Inclusions in generalized Orlicz spaces.Bull. Iran. Math. Soc. 47 (2021), 1227-1233. Zbl 07377360, MR 4278242, 10.1007/s41980-020-00437-y; reference:[5] Subramanian, B.: On the inclusion $L^p(\mu)\subset L^q(\mu)$.Am. Math. Mon. 85 (1978), 479-481. Zbl 0388.46021, MR 0482134, 10.2307/2320071; reference:[6] Villani, A.: Another note on the inclusion $L^p(\mu) \subset L^q(\mu)$.Am. Math. Mon. 92 (1985), 485-487. Zbl 0592.46028, MR 0801221, 10.2307/2322503

الاتاحة: http://hdl.handle.net/10338.dmlcz/151527

المؤلفون: Sin, Cholmin, Ri, Sin-Il

مصطلحات موضوعية: keyword:existence of weak solutions, keyword:electrorheological fluid, keyword:Lipschitz truncation, keyword:variable exponent, msc:35A23, msc:35D30, msc:46E30, msc:46E35, msc:76A05, msc:76D03

وصف الملف: application/pdf

Relation: mr:MR4512174; zbl:Zbl 07655827; reference:[1] Abbatiello, A., Crispo, F., Maremonti, P.: Electrorheological fluids: Ill posedness of uniqueness backward in time.Nonlinear Anal., Theory Methods Appl., Ser. A 170 (2018), 47-69. Zbl 1469.35172, MR 3765555, 10.1016/j.na.2017.12.014; reference:[2] Bauer, S., Pauly, D.: On Korn's first inequality for mixed tangential and normal boundary conditions on bounded Lipschitz domains in $\mathbb{R}^N$.Ann. Univ. Ferrara, Sez. VII, Sci. Mat. 62 (2016), 173-188. Zbl 1364.46028, MR 3570353, 10.1007/s11565-016-0247-x; reference:[3] Veiga, H. Beirão da: Regularity for Stokes and generalized Stokes systems under nonhomogeneous slip-type boundary conditions.Adv. Differ. Equ. 9 (2004), 1079-1114. Zbl 1103.35084, MR 2098066; reference:[4] Veiga, H. Beirão da: On the regularity of flows with Ladyzhenskaya shear-dependent viscosity and slip or non-slip boundary conditions.Commun. Pure Appl. Math. 58 (2005), 552-577. 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الاتاحة: http://hdl.handle.net/10338.dmlcz/151099

المؤلفون: Ren, Yanbo, Ding, Shuang

مصطلحات موضوعية: keyword:weight, keyword:weak type inequality, keyword:Hardy-Littlewood maximal function, keyword:Orlicz class, msc:42B25, msc:46E30

وصف الملف: application/pdf

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الاتاحة: http://hdl.handle.net/10338.dmlcz/149574

المؤلفون: Karlovich, Alexei, Shargorodsky, Eugene

مصطلحات موضوعية: keyword:Lorentz Gamma space, keyword:reflexivity, keyword:Boyd indices, keyword:Zippin indices, msc:42B25, msc:46E30

وصف الملف: application/pdf

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الاتاحة: http://hdl.handle.net/10338.dmlcz/149249

المؤلفون: Shi, Siyu, Shi, Zhongrui, Wu, Shujun

مصطلحات موضوعية: keyword:compact set, keyword:weak topology, keyword:Banach space, keyword:dual space, keyword:Orlicz sequence spaces, msc:46B20, msc:46E30

وصف الملف: application/pdf

Relation: mr:MR4339103; zbl:Zbl 07442466; reference:[1] Aleksandrov, P. S., Kolmogorov, A. N.: Introduction to the Theory of Sets and the Theory of Functions. 1. Introduction to the General Theory of Sets and Functions.Gosudarstv. Izdat. Tehn.-Teor. Lit., Moscow (1948), Russian. Zbl 0037.03404, MR 0040369; reference:[2] Andô, T.: Weakly compact sets in Orlicz spaces.Can. J. Math. 14 (1962), 170-176. Zbl 0103.32902, MR 0157228, 10.4153/CJM-1962-012-7; reference:[3] Arzelà, C.: Funzioni di linee.Rom. Acc. L. Rend. (4) 5 (1889), 342-348 Italian \99999JFM99999 21.0424.01.; reference:[4] Batt, J., Schlüchtermann, G.: Eberlein compacts in $L_1(X)$.Stud. Math. 83 (1986), 239-250. Zbl 0555.46014, MR 0850826, 10.4064/sm-83-3-239-250; reference:[5] Brouwer, L. E. J.: Beweis der Invarianz des $n$-dimensionalen Gebiets.Math. Ann. 71 (1911), 305-313 German \99999JFM99999 42.0418.01. MR 1511658, 10.1007/BF01456846; reference:[6] Cheng, L., Cheng, Q., Shen, Q., Tu, K., Zhang, W.: A new approach to measures of noncompactness of Banach spaces.Stud. Math. 240 (2018), 21-45. Zbl 06828572, MR 3719465, 10.4064/sm8448-2-2017; reference:[7] Cheng, L., Cheng, Q., Zhang, J.: On super fixed point property and super weak compactness of convex subsets in Banach spaces.J. Math. Anal. Appl. 428 (2015), 1209-1224. Zbl 1329.46015, MR 3334975, 10.1016/j.jmaa.2015.03.061; reference:[8] Darbo, G.: Punti uniti in trasformazioni a codominio non compatto.Rend. Sem. Mat. Univ. Padova 24 (1955), 84-92 Italian. Zbl 0064.35704, MR 0070164; reference:[9] Dodds, P. G., Sukochev, F. A., Schlüchtermann, G.: Weak compactness criteria in symmetric spaces of measurable operators.Math. Proc. Camb. Philos. Soc. 131 (2001), 363-384. Zbl 1004.46038, MR 1857125, 10.1017/S0305004101005114; reference:[10] Fabian, M., Montesinos, V., Zizler, V.: On weak compactness in $L_1$ spaces.Rocky Mt. J. Math. 39 (2009), 1885-1893. Zbl 1190.46011, MR 2575884, 10.1216/RMJ-2009-39-6-1885; reference:[11] Foralewski, P., Hudzik, H., Kolwicz, P.: Non-squareness properties of Orlicz-Lorentz sequence spaces.J. Funct. Anal. 264 (2013), 605-629. Zbl 1263.46015, MR 2997393, 10.1016/j.jfa.2012.10.014; reference:[12] Gale, D.: The game of Hex and the Brouwer fixed-point theorem.Am. Math. Mon. 86 (1979), 818-827. Zbl 0448.90097, MR 0551501, 10.2307/2320146; reference:[13] James, R. C.: Weakly compact sets.Trans. Am. Math. Soc. 113 (1964), 129-140. Zbl 0129.07901, MR 0165344, 10.1090/S0002-9947-1964-0165344-2; reference:[14] James, R. C.: The Eberlein-Šmulian theorem.Functional Analysis. Selected Topics Narosa Publishing House, New Delhi (1998), 47-49. Zbl 1010.46011, MR 1668790; reference:[15] Kelley, J. L.: General Topology.The University Series in Higher Mathematics. D. van Nostrand, New York (1955). Zbl 0066.16604, MR 0070144; reference:[16] Kolmogorov, A. N., Tikhomirov, V. M.: $\epsilon$-entropy and $\epsilon$-capacity of sets in function spaces.Usp. Mat. Nauk 14 (1959), 3-86 Russian. Zbl 0090.33503, MR 0112032; reference:[17] Krasnosel'skij, M. A., Rutitskij, Y. B.: Convex Functions and Orlicz Spaces.P. Noordhoff, Groningen (1961). Zbl 0095.09103, MR 0126722; reference:[18] Leray, J., Schauder, J.: Topologie et équations fonctionnelles.Ann. Sci. Éc. Norm. Supér., III. Ser. 51 (1934), 45-78 French. Zbl 0009.07301, MR 1509338, 10.24033/asens.836; reference:[19] Musielak, J.: Orlicz Spaces and Modular Spaces.Lecture Notes in Mathematics 1034. Springer, Berlin (1983). Zbl 0557.46020, MR 0724434, 10.1007/BFb0072210; reference:[20] Schlüchtermann, G.: Weak compactness in $L_\infty(\mu,X)$.J. Funct. Anal. 125 (1994), 379-388. Zbl 0828.46036, MR 1297673, 10.1006/jfan.1994.1129; reference:[21] Shi, S., Shi, Z.: On generalized Young's inequality.Function Spaces XII Banach Center Publications 119. Polish Academy of Sciences, Institute of Mathematics. Warsaw (2019), 295-309. Zbl 1444.46024, 10.4064/bc119-17; reference:[22] Shi, Z., Wang, Y.: Uniformly non-square points and representation of functionals of Orlicz-Bochner sequence spaces.Rocky Mt. J. Math. 48 (2018), 639-660. Zbl 1402.46013, MR 3810210, 10.1216/RMJ-2018-48-2-639; reference:[23] Šmulian, V.: On compact sets in the space of measurable functions.Mat. Sb., N. Ser. 15 (1944), 343-346 Russian. Zbl 0060.27602, MR 0012210; reference:[24] Wu, Y.: Normed compact sets and weakly $H$-compact in Orlicz space.J. Nature 3 (1982), 234 Chinese.; reference:[25] Wu, C., Wang, T.: Orlicz Spaces and Applications.Heilongjiang Sci. & Tech. Press, Harbin (1983), Chinese.; reference:[26] Zhang, X., Shi, Z.: A criterion of compact set in Orlicz sequence space $l_{(M)}$.J. Changchun Post Telcommunication Institute 15 (1997), 64-67 Chinese.

الاتاحة: http://hdl.handle.net/10338.dmlcz/149230

المؤلفون: Hassaine, Slimane, Boulahia, Fatiha

مصطلحات موضوعية: keyword:Besicovitch--Orlicz space, keyword:extreme point, keyword:strict convexity, keyword:almost periodic function, msc:39A24, msc:46B20, msc:46E30

وصف الملف: application/pdf

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الاتاحة: http://hdl.handle.net/10338.dmlcz/148939

المؤلفون: Maeda, Fumi-Yuki, Mizuta, Yoshihiro, Ohno, Takao, Shimomura, Tetsu

مصطلحات موضوعية: keyword:Riesz potential, keyword:Trudinger's inequality, keyword:Musielak-Orlicz-Morrey space, keyword:double phase functional, msc:31C15, msc:46E30

وصف الملف: application/pdf

Relation: mr:MR4263183; zbl:07361082; reference:[1] Adams, D. R., Hedberg, L. I.: Function Spaces and Potential Theory.Grundlehren der Mathematischen Wissenschaften 314. Springer, Berlin (1996). Zbl 0834.46021, MR 1411441, 10.1007/978-3-662-03282-4; reference:[2] Ahmida, Y., Chlebicka, I., Gwiazda, P., Youssfi, A.: Gossez's approximation theorems in Musielak-Orlicz-Sobolev spaces.J. Funct. Anal. 275 (2018), 2538-2571. Zbl 1405.42042, MR 3847479, 10.1016/j.jfa.2018.05.015; reference:[3] Baroni, P., Colombo, M., Mingione, G.: Non-autonomous functionals, borderline cases and related function classes.St. Petersbg. Math. J. 27 (2016), 347-379. Zbl 1335.49057, MR 3570955, 10.1090/spmj/1392; reference:[4] Baroni, P., Colombo, M., Mingione, G.: Regularity for general functionals with double phase.Calc. Var. Partial Differ. Equ. 57 (2018), Article ID 62, 48 pages. Zbl 1394.49034, MR 3775180, 10.1007/s00526-018-1332-z; reference:[5] Colombo, M., Mingione, G.: Bounded minimisers of double phase variational integrals.Arch. Ration. Mech. Anal. 218 (2015), 219-273. Zbl 1325.49042, MR 3360738, 10.1007/s00205-015-0859-9; reference:[6] Colombo, M., Mingione, G.: Regularity for double phase variational problems.Arch. Ration. Mech. Anal. 215 (2015), 443-496. Zbl 1322.49065, MR 3294408, 10.1007/s00205-014-0785-2; reference:[7] Futamura, T., Mizuta, Y.: Continuity properties of Riesz potentials for functions in $L^{p(\cdot)}$ of variable exponent.Math. Inequal. Appl. 8 (2005), 619-631. Zbl 1087.31004, MR 2174890, 10.7153/mia-08-58; reference:[8] Futamura, T., Mizuta, Y., Shimomura, T.: Sobolev embedding for variable exponent Riesz potentials on metric spaces.Ann. Acad. Sci. Fenn., Math. 31 (2006), 495-522. Zbl 1100.31002, MR 2248828; reference:[9] Futamura, T., Mizuta, Y., Shimomura, T.: Integrability of maximal functions and Riesz potentials in Orlicz spaces of variable exponent.J. Math. Anal. Appl. 366 (2010), 391-417. Zbl 1193.46016, MR 2600488, 10.1016/j.jmaa.2010.01.053; reference:[10] Hästö, P.: The maximal operator on generalized Orlicz spaces.J. Funct. Anal. 269 (2015), 4038-4048 corrigendum ibid. 271 240-243 2016. Zbl 1338.47032, MR 3418078, 10.1016/j.jfa.2015.10.002; reference:[11] Maeda, F.-Y., Mizuta, Y., Ohno, T., Shimomura, T.: Boundedness of maximal operators and Sobolev's inequality on Musielak-Orlicz-Morrey spaces.Bull. Sci. Math. 137 (2013), 76-96. Zbl 1267.46045, MR 3007101, 10.1016/j.bulsci.2012.03.008; reference:[12] Maeda, F.-Y., Mizuta, Y., Ohno, T., Shimomura, T.: Trudinger's inequality and continuity of potentials on Musielak-Orlicz-Morrey spaces.Potential Anal. 38 (2013), 515-535. Zbl 1268.46024, MR 3015362, 10.1007/s11118-012-9284-y; reference:[13] Maeda, F.-Y., Mizuta, Y., Ohno, T., Shimomura, T.: Sobolev's inequality for double phase functionals with variable exponents.Forum Math. 31 (2019), 517-527. Zbl 1423.46049, MR 3918454, 10.1515/forum-2018-0077; reference:[14] Mizuta, Y., Nakai, E., Ohno, T., Shimomura, T.: Riesz potentials and Sobolev embeddings on Morrey spaces of variable exponents.Complex Var. Elliptic Equ. 56 (2011), 671-695. Zbl 1228.31004, MR 2832209, 10.1080/17476933.2010.504837; reference:[15] Mizuta, Y., Ohno, T., Shimomura, T.: Sobolev embeddings for Riesz potential spaces of variable exponents near 1 and Sobolev's exponent.Bull. Sci. Math. 134 (2010), 12-36. Zbl 1192.46027, MR 2579870, 10.1016/j.bulsci.2009.09.004; reference:[16] Mizuta, Y., Shimomura, T.: Differentiability and Hölder continuity of Riesz potentials of Orlicz functions.Analysis, München 20 (2000), 201-223. Zbl 0955.31002, MR 1778254, 10.1524/anly.2000.20.3.201; reference:[17] Mizuta, Y., Shimomura, T.: Sobolev embeddings for Riesz potentials of functions in Morrey spaces of variable exponent.J. Math. Soc. Japan 60 (2008), 583-602. Zbl 1161.46305, MR 2421989, 10.2969/jmsj/06020583; reference:[18] Musielak, J.: Orlicz Spaces and Modular Spaces.Lecture Notes in Mathematics 1034. Springer, Berlin (1983). Zbl 0557.46020, MR 0724434, 10.1007/BFb0072210; reference:[19] Nakai, E.: Generalized fractional integrals on Orlicz-Morrey spaces.Banach and Function Spaces Yokohama Publishers, Yokohama (2004), 323-333. Zbl 1118.42005, MR 2146936; reference:[20] Ohno, T., Shimomura, T.: Trudinger's inequality for Riesz potentials of functions in Musielak-Orlicz spaces.Bull. Sci. Math. 138 (2014), 225-235. Zbl 1305.46022, MR 3175020, 10.1016/j.bulsci.2013.05.007

الاتاحة: http://hdl.handle.net/10338.dmlcz/148918

المؤلفون: Djabri, Yousra, Bedouhene, Fazia, Boulahia, Fatiha

مصطلحات موضوعية: keyword:Bohr almost periodic, keyword:Bochner transform, keyword:Stepanov--Orlicz almost periodic function, keyword:semilinear evolution equations, keyword:Nemytskii operator, msc:34C27, msc:35B15, msc:46E30

وصف الملف: application/pdf

Relation: mr:MR4186113; zbl:Zbl 07286010; reference:[1] Albrycht J.: The theory of Marcinkiewic–Orlicz spaces.Rozprawy Mat. 27 (1962), 56 pages. MR 0139935; reference:[2] Amerio L., Prouse G.: Almost-Periodic Functions and Functional Equations.Van Nostrand Reinhold, New York, Ont.-Melbourne, 1971. MR 0275061; reference:[3] Andres J., Bersani A. M., Grande R. F.: Hierarchy of almost-periodic function spaces.Rend. Mat. Appl. (7) 26 (2006), no. 2, 121–188. Zbl 1133.42002, MR 2275292; reference:[4] Andres J., Pennequin D.: On Stepanov almost-periodic oscillations and their discretizations.J. Difference Equ. Appl. 18 (2012), no. 10, 1665–1682. MR 2979829, 10.1080/10236198.2011.587813; reference:[5] Andres J., Pennequin D.: On the nonexistence of purely Stepanov almost-periodic solutions of ordinary differential equations.Proc. Amer. Math. Soc. 140 (2012), no. 8, 2825–2834. 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الاتاحة: http://hdl.handle.net/10338.dmlcz/148472

المؤلفون: Karapetyants, Alexey, Restrepo, Joel Esteban

مصطلحات موضوعية: keyword:Hölder space, keyword:harmonic function, keyword:variable exponent space, keyword:modulus of continuity, msc:42B35, msc:46E15, msc:46E30

وصف الملف: application/pdf

Relation: mr:MR4151698; zbl:07250682; reference:[1] Arsenović, M., Kojić, V., Mateljević, M.: On Lipschitz continuity of harmonic quasiregular maps on the unit ball in $\mathbb R^n$.Ann. Acad. Sci. Fenn., Math. 33 (2008), 315-318. Zbl 1140.31003, MR 2386855; reference:[2] Axler, S., Bourdon, P., Ramey, W.: Harmonic Function Theory.Graduate Texts in Mathematics 137, Springer, New York (2001). Zbl 0959.31001, MR 1805196, 10.1007/b97238; reference:[3] Blumenson, L. E.: A derivation of $n$-dimensional spherical coordinates.Am. Math. Mon. 67 (1960), 63-66. MR 1530579, 10.2307/2308932; reference:[4] Chacón, G. R., Rafeiro, H.: Variable exponent Bergman spaces.Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 105 (2014), 41-49. Zbl 1288.30059, MR 3200739, 10.1016/j.na.2014.04.001; reference:[5] Chacón, G. R., Rafeiro, H.: Toeplitz operators on variable exponent Bergman spaces.Mediterr. J. Math. 13 (2016), 3525-3536. Zbl 1354.30049, MR 3554324, 10.1007/s00009-016-0701-0; reference:[6] Cruz-Uribe, D., Fiorenza, A.: Variable Lebesgue Spaces: Foundations and Harmonic Analysis.Applied and Numerical Harmonic Analysis, Birkhäuser/Springer, Heidelberg (2013). Zbl 1268.46002, MR 3026953, 10.1007/978-3-0348-0548-3; reference:[7] Diening, L., Harjulehto, P., Hästö, P., Růžička, M.: Lebesgue and Sobolev Spaces with Variable Exponents.Lecture Notes in Mathematics 2017, Springer, Berlin (2011). Zbl 1222.46002, MR 2790542, 10.1007/978-3-642-18363-8; reference:[8] Duren, P., Schuster, A.: Bergman Spaces.Mathematical Surveys and Monographs 100, American Mathematical Society, Providence (2004). Zbl 1059.30001, MR 2033762, 10.1090/surv/100; reference:[9] Hedenmalm, H., Korenblum, B., Zhu, K.: Theory of Bergman Spaces.Graduate Texts in Mathematics 199, Springer, New York (2000). Zbl 0955.32003, MR 1758653, 10.1007/978-1-4612-0497-8; reference:[10] Karapetyants, A., Rafeiro, H., Samko, S.: Boundedness of the Bergman projection and some properties of Bergman type spaces.Complex Anal. Oper. Theory 13 (2019), 275-289. Zbl 1421.30070, MR 3905593, 10.1007/s11785-018-0780-y; reference:[11] Karapetyants, A., Samko, S.: Spaces $ BMO_{p(\cdot)}(\Bbb D)$ of a variable exponent $p(z)$.Georgian Math. J. 17 (2010), 529-542. Zbl 1201.30072, MR 2719633, 10.1515/gmj.2010.028; reference:[12] Karapetyants, A., Samko, S.: Mixed norm Bergman-Morrey-type spaces on the unit disc.Math. Notes 100 (2016), 38-48. Zbl 1364.30063, MR 3588827, 10.1134/S000143461607004X; reference:[13] Karapetyants, A., Samko, S.: Mixed norm variable exponent Bergman space on the unit disc.Complex Var. Elliptic Equ. 61 (2016), 1090-1106. Zbl 1351.30042, MR 3500518, 10.1080/17476933.2016.1140750; reference:[14] Karapetyants, A., Samko, S.: Mixed norm spaces of analytic functions as spaces of generalized fractional derivatives of functions in Hardy type spaces.Fract. Calc. Appl. Anal. 20 (2017), 1106-1130. Zbl 1386.30052, MR 3721891, 10.1515/fca-2017-0059; reference:[15] Karapetyants, A., Samko, S.: On boundedness of Bergman projection operators in Banach spaces of holomorphic functions in half-plane and harmonic functions in half-space.J. Math. Sci., New York 226 (2017), 344-354. Zbl 1386.30051, MR 3705149, 10.1007/s10958-017-3538-6; reference:[16] Karapetyants, A., Samko, S.: Generalized Hölder spaces of holomorphic functions in domains in the complex plane.Mediterr. J. Math. 15 (2018), Paper No. 226, 17 pages. Zbl 1411.30039, MR 3878666, 10.1007/s00009-018-1272-z; reference:[17] Karapetyants, A., Samko, S.: On mixed norm Bergman-Orlicz-Morrey spaces.Georgian Math. J. 25 (2018), 271-282. Zbl 1392.30023, MR 3808288, 10.1515/gmj-2018-0027; reference:[18] Kokilashvili, V., Meskhi, A., Rafeiro, H., Samko, S.: Integral Operators in Non-Standard Function Spaces. Volume 1. Variable Exponent Lebesgue and Amalgam Spaces.Operator Theory: Advances and Applications 248, Birkhäuser/Springer, Basel (2016). Zbl 1385.47001, MR 3559400, 10.1007/978-3-319-21015-5; reference:[19] Kokilashvili, V., Meskhi, A., Rafeiro, H., Samko, S.: Integral Operators in Non-Standard Function Spaces. Volume 2. Variable Exponent Hölder, Morrey-Campanato and Grand Spaces.Operator Theory: Advances and Applications 249, Birkhäuser/Springer, Basel (2016). Zbl 1367.47004, MR 3559401, 10.1007/978-3-319-21018-6; reference:[20] Zhu, K.: Spaces of Holomorphic Functions in the Unit Ball.Graduate texts in Mathematics 226, Springer, New York (2005). Zbl 1067.32005, MR 2115155, 10.1007/0-387-27539-8; reference:[21] Zhu, K.: Operator Theory in Function Spaces.Mathematical Surveys and Monographs 138, American Mathematical Society, Providence (2007). Zbl 1123.47001, MR 2311536, 10.1090/surv/138

الاتاحة: http://hdl.handle.net/10338.dmlcz/148321

المؤلفون: Ruan, Jianmiao, Fan, Dashan, Li, Hongliang

مصطلحات موضوعية: keyword:Hausdorff operator, keyword:Morrey space, keyword:Campanato space, msc:42B30, msc:42B35, msc:46E30

وصف الملف: application/pdf

Relation: mr:MR4111856; zbl:07217148; reference:[1] Chen, J., Fan, D., Li, J.: Hausdorff operators on function spaces.Chin. Ann. Math., Ser. B 33 (2012), 537-556. Zbl 1261.42036, MR 2996530, 10.1007/s11401-012-0724-1; reference:[2] Chen, J., Fan, D., Wang, S.: Hausdorff operators on Euclidean spaces.Appl. Math., Ser. B (Engl. Ed.) 28 (2013), 548-564. Zbl 1299.42078, MR 3143905, 10.1007/s11766-013-3228-1; reference:[3] Chen, J., Zhu, X.: Boundedness of multidimensional Hausdorff operators on $H^{1}(R^{n})$.J. Math. Anal. Appl. 409 (2014), 428-434. Zbl 1309.42026, MR 3095051, 10.1016/j.jmaa.2013.07.042; reference:[4] Fefferman, C., Stein, E. M.: $H^p$ spaces of several variables.Acta Math. 129 (1972), 137-193. Zbl 0257.46078, MR 0447953, 10.1007/BF02392215; reference:[5] Fu, Z., Grafakos, L., Lu, S., Zhao, F.: Sharp bounds for $m$-linear Hardy and Hilbert operators.Houston J. Math. 38 (2012), 225-244. Zbl 1248.42020, MR 2917283; reference:[6] Lerner, A. K., Liflyand, E.: Multidimensional Hausdorff operators on the real Hardy space.J. Aust. Math. Soc. 83 (2007), 79-86. Zbl 1143.47023, MR 2378435, 10.1017/S1446788700036399; reference:[7] Liflyand, E.: Open problems on Hausdorff operators.Complex Analysis and Potential Theory World Scientific, Hackensack (2007), 280-285. Zbl 1156.30002, MR 2368363, 10.1142/9789812778833_0030; reference:[8] Liflyand, E.: Boundedness of multidimensional Hausdorff operators on $H^1({\mathbb R}^n)$.Acta Sci. Math. 74 (2008), 845-851. Zbl 1199.47155, MR 2487949; reference:[9] Liflyand, E.: Hausdorff operators on Hardy spaces.Eurasian Math. J. 4 (2013), 101-141. Zbl 1328.47039, MR 3382905; reference:[10] Liflyand, E., Miyachi, A.: Boundedness of the Hausdorff operators in $H^p$ spaces, $0; reference:[11] Liflyand, E., Móricz, F.: The Hausdorff operator is bounded on the real Hardy space $H^1({\mathbb R})$.Proc. Am. Math. Soc. 128 (2000), 1391-1396. Zbl 0951.47038, MR 1641140, 10.1090/S0002-9939-99-05159-X; reference:[12] Liflyand, E., Móricz, F.: Commuting relations for Hausdorff operators and Hilbert transforms on real Hardy spaces.Acta Math. Hung. 97 (2002), 133-143. Zbl 1012.47011, MR 1932800, 10.1023/A:1020867130612; reference:[13] Móricz, F.: Multivariate Hausdorff operators on the spaces $H^{1}({\mathbb R}^{n})$ and ${\rm BMO({\mathbb R}^{n})}$.Anal. Math. 31 (2005), 31-41. Zbl 1093.47036, MR 2145404, 10.1007/s10476-005-0003-4; reference:[14] Ruan, J., Fan, D.: Hausdorff operators on the power weighted Hardy spaces.J. Math. Anal. Appl. 433 (2016), 31-48. Zbl 1331.42018, MR 3388780, 10.1016/j.jmaa.2015.07.062; reference:[15] Ruan, J., Fan, D., Wu, Q.: Weighted Herz space estimates for Hausdorff operators on the Heisenberg group.Banach J. Math. Anal. 11 (2017), 513-535. Zbl 1370.42020, MR 3679894, 10.1215/17358787-2017-0004; reference:[16] Weisz, F.: The boundedness of the Hausdorff operator on multi-dimensional Hardy spaces.Analysis, München 24 (2004), 183-195. Zbl 1071.47033, MR 2085955, 10.1524/anly.2004.24.14.183; reference:[17] Xiao, J.: $L^{p}$ and BMO bounds of weighted Hardy-Littlewood averages.J. Math. Anal. Appl. 262 (2001), 660-666. Zbl 1009.42013, MR 1859331, 10.1006/jmaa.2001.7594

الاتاحة: http://hdl.handle.net/10338.dmlcz/148242

المؤلفون: Youssfi, Ahmed, Ahmida, Youssef

مصطلحات موضوعية: keyword:approximate identity, keyword:Musielak-Orlicz space, keyword:density of smooth functions, msc:46B10, msc:46E30

وصف الملف: application/pdf

Relation: mr:MR4111853; zbl:07217145; reference:[1] Adams, R. A., Fournier, J. J. F.: Sobolev Spaces.Pure and Applied Mathematics 140, Academic Press, New York (2003). Zbl 1098.46001, MR 2424078, 10.1016/S0079-8169(13)62896-2; reference:[2] Benkirane, A., Douieb, J., Val, M. Ould Mohamedhen: An approximation theorem in Musielak-Orlicz-Sobolev spaces.Commentat. Math. 51 (2011), 109-120. Zbl 1294.46025, MR 2849685, 10.14708/cm.v51i1.5313; reference:[3] Benkirane, A., Val, M. Ould Mohamedhen: Some approximation properties in Musielak-Orlicz-Sobolev spaces.Thai J. Math. 10 (2012), 371-381. Zbl 1264.46024, MR 3001860; reference:[4] Bennett, C., Sharpley, R.: Interpolation of Operators.Pure and Applied Mathematics 129, Academic Press, Boston (1988). Zbl 0647.46057, MR 0928802, 10.1016/S0079-8169(13)62909-8; reference:[5] Cruz-Uribe, D., Fiorenza, A.: Approximate identities in variable $L^{p}$ spaces.Math. Nachr. 280 (2007), 256-270. Zbl 1178.42022, MR 2292148, 10.1002/mana.200410479; reference:[6] Diening, L., Harjulehto, P., Hästö, P., Růžička, M.: Lebesgue and Sobolev Spaces with Variable Exponents.Lecture Notes in Mathematics 2017, Springer, Berlin (2011). Zbl 1222.46002, MR 2790542, 10.1007/978-3-642-18363-8; reference:[7] Hudzik, H.: A generalization of Sobolev spaces. II.Funct. Approximatio, Comment. Math. 3 (1976), 77-85. Zbl 0355.46011, MR 0467279; reference:[8] Kamińska, A.: On some compactness criterion for Orlicz subspace $E_{\Phi}(\Omega)$.Ann. Soc. Math. Pol., Ser. I, Commentat. Math. 22 (1981), 245-255. Zbl 0504.46024, MR 0641438, 10.14708/cm.v22i2.6021; reference:[9] Kamińska, A.: Some convexity properties of Musielak-Orlicz spaces of Bochner type.Rend. Circ. Mat. Palermo, II. Ser. Suppl. 10 (1985), 63-73. Zbl 0609.46015, MR 0894273; reference:[10] Kamińska, A., Hudzik, H.: Some remarks on convergence in Orlicz space.Commentat. Math. 21 (1980), 81-88. Zbl 0436.46022, MR 0577673, 10.14708/cm.v21i1.5965; reference:[11] Kamińska, A., Kubiak, D.: The Daugavet property in the Musielak-Orlicz spaces.J. Math. Anal. Appl. 427 (2015), 873-898. Zbl 1325.46012, MR 3323013, 10.1016/j.jmaa.2015.02.035; reference:[12] Kováčik, O., Rákosník, J.: On spaces $L^{p(x)}$ and $W^{k,p(x)}$.Czech. Math. J. 41 (1991), 592-618. Zbl 0784.46029, MR 1134951, 10.21136/CMJ.1991.102493; reference:[13] Krasnosel'skiĭ, M. A., Rutitskiĭ, J. B.: Convex Functions and Orlicz Spaces.P. Noordhoff, Groningen (1961). Zbl 0095.09103, MR 0126722; reference:[14] Kufner, A., John, O., Fučík, S.: Function Spaces.Monographs and Textbooks on Mechanics of Solids and Fluids. Mechanics: Analysis, Noordhoff International Publishing, Leyden; Academia, Prague (1977). Zbl 0364.46022, MR 0482102; reference:[15] Musielak, J.: Orlicz Spaces and Modular Spaces.Lecture Notes in Mathematics 1034, Springer, Berlin (1983). Zbl 0557.46020, MR 0724434, 10.1007/BFb0072210; reference:[16] Nakano, H.: Modulared Semi-Ordered Linear Spaces.Tokyo Math. Book Series 1, Maruzen, Tokyo (1950). Zbl 0041.23401, MR 0038565; reference:[17] Orlicz, W.: Über konjugierte Exponentenfolgen.Studia Math. German 3 (1931), 200-211. Zbl 0003.25203, 10.4064/sm-3-1-200-211

الاتاحة: http://hdl.handle.net/10338.dmlcz/148239

المؤلفون: Chacón, Gerardo R., Chacón, Gerardo A.

مصطلحات موضوعية: keyword:Fock space, keyword:variable exponent Lebesgue space, keyword:Bergman projection, msc:30H20, msc:46E30

وصف الملف: application/pdf

Relation: mr:MR4078353; zbl:07217128; reference:[1] Chacón, G. R., Rafeiro, H.: Variable exponent Bergman spaces.Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 105 (2014), 41-49. Zbl 1288.30059, MR 3200739, 10.1016/j.na.2014.04.001; reference:[2] Chacón, G. R., Rafeiro, H.: Toeplitz operators on variable exponent Bergman spaces.Mediterr. J. Math. 13 (2016), 3525-3536. Zbl 1354.30049, MR 3554324, 10.1007/s00009-016-0701-0; reference:[3] Chacón, G. R., Rafeiro, H., Vallejo, J. C.: Carleson measures for variable exponent Bergman spaces.Complex Anal. Oper. Theory 11 (2017), 1623-1638. Zbl 1387.30081, MR 3702967, 10.1007/s11785-016-0573-0; reference:[4] Cruz-Uribe, D. V., Fiorenza, A.: Variable Lebesgue Spaces. Foundations and Harmonic Analysis.Applied and Numerical Harmonic Analysis, Birkhäuser, Basel (2013). Zbl 1268.46002, MR 3026953, 10.1007/978-3-0348-0548-3; reference:[5] Diening, L., Harjulehto, P., Hästö, P., Růžička, M.: Lebesgue and Sobolev Spaces with Variable Exponents.Lecture Notes in Mathematics 2017, Springer, Berlin (2011). Zbl 1222.46002, MR 2790542, 10.1007/978-3-642-18363-8; reference:[6] Harjulehto, P., Hästö, P., Klén, R.: Generalized Orlicz spaces and related PDE.Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 143 (2016), 155-173. Zbl 1360.46029, MR 3516828, 10.1016/j.na.2016.05.002; reference:[7] Isralowitz, J.: Invertible Toeplitz products, weighted norm inequalities, and $ A_p$ weights.J. Oper. Theory 71 (2014), 381-410. Zbl 1313.47059, MR 3214643, 10.7900/jot.2012apr10.1989; reference:[8] Karapetyants, A., Samko, S.: Spaces $ BMO^{p(\cdot)}(\mathbb D)$ of a variable exponent $p(z)$.Georgian Math. J. 17 (2010), 529-542. Zbl 1201.30072, MR 2719633, 10.1515/GMJ.2010.028; reference:[9] Karapetyants, A. N., Samko, S. G.: Mixed norm Bergman-Morrey-type spaces on the unit disc.Math. Notes 100 (2016), 38-48 translation from Mat. Zametki 100 2016 47-58. Zbl 1364.30063, MR 3588827, 10.1134/S000143461607004X; reference:[10] Karapetyants, A. N., Samko, S. G.: Mixed norm variable exponent Bergman space on the unit disc.Complex Var. Elliptic Equ. 61 (2016), 1090-1106. Zbl 1351.30042, MR 3500518, 10.1080/17476933.2016.1140750; reference:[11] Kokilashvili, V., Paatashvili, V.: On Hardy classes of analytic functions with a variable exponent.Proc. A. Razmadze Math. Inst. 142 (2006), 134-137. Zbl 1126.47031, MR 2294576; reference:[12] Kokilashvili, V., Paatashvili, V.: On the convergence of sequences of functions in Hardy classes with a variable exponent.Proc. A. Razmadze Math. Inst. 146 (2008), 124-126. Zbl 1166.47033, MR 2464049; reference:[13] Kováčik, O., Rákosník, J.: On spaces $L^{p(x)}$ and $W^{k,p(x)}$.Czech. Math. J. 41 (1991), 592-618. Zbl 0784.46029, MR 1134951, 10.21136/CMJ.1991.102493; reference:[14] Lefèvre, P., Li, D., Queffélec, H., Rodríguez-Piazza, L.: Composition operators on Hardy-Orlicz spaces.Mem. Am. Math. Soc. 207 (2010), 74 pages. Zbl 1200.47035, MR 2681410, 10.1090/S0065-9266-10-00580-6; reference:[15] Lefèvre, P., Li, D., Queffélec, H., Rodríguez-Piazza, L.: Compact composition operators on Bergman-Orlicz spaces.Trans. Am. Math. Soc. 365 (2013), 3943-3970. Zbl 1282.47033, MR 3055685, 10.1090/S0002-9947-2013-05922-3; reference:[16] Motos, J., Planells, M. J., Talavera, C. F.: On variable exponent Lebesgue spaces of entire analytic functions.J. Math. Anal. Appl. 388 (2012), 775-787. Zbl 1244.46008, MR 2869787, 10.1016/j.jmaa.2011.09.069; reference:[17] Orlicz, W.: Über konjugierte Exponentenfolgen.Stud. Math. 3 (1931), 200-211 German. Zbl 0003.25203, 10.4064/sm-3-1-200-211; reference:[18] Tung, Y.-C. J.: Fock Spaces.Ph.D. Thesis, The University of Michigan (2005). MR 2706955; reference:[19] Zhu, K.: Analysis on Fock Spaces.Graduate Texts in Mathematics 263, Springer, New York (2012). Zbl 1262.30003, MR 2934601, 10.1007/978-1-4419-8801-0

الاتاحة: http://hdl.handle.net/10338.dmlcz/148049

المؤلفون: Sato, Shuichi

مصطلحات موضوعية: keyword:Littlewood-Paley function, keyword:non-isotropic dilation, msc:42B25, msc:46E30

وصف الملف: application/pdf

Relation: mr:MR3959948; zbl:Zbl 07088788; reference:[1] Benedek, A., Calderón, A. P., Panzone, R.: Convolution operators on Banach space valued functions.Proc. Natl. Acad. Sci. USA 48 (1962), 356-365. Zbl 0103.33402, MR 0133653, 10.1073/pnas.48.3.356; reference:[2] Calderón, A. P.: Inequalities for the maximal function relative to a metric.Stud. Math. 57 (1976), 297-306. Zbl 0341.44007, MR 0442579, 10.4064/sm-57-3-297-306; reference:[3] Calderón, A. P., Torchinsky, A.: Parabolic maximal functions associated with a distribution.Adv. Math. 16 (1975), 1-64. Zbl 0315.46037, MR 0417687, 10.1016/0001-8708(75)90099-7; reference:[4] Capri, O. N.: On an inequality in the theory of parabolic $H^p$ spaces.Rev. Unión Mat. Argent. 32 (1985), 17-28. Zbl 0643.42013, MR 0873913; reference:[5] Cheng, L. C.: On Littlewood-Paley functions.Proc. Am. Math. Soc. 135 (2007), 3241-3247. Zbl 1124.42013, MR 2322755, 10.1090/S0002-9939-07-08917-4; reference:[6] Ding, Y., Sato, S.: Littlewood-Paley functions on homogeneous groups.Forum Math. 28 (2016), 43-55. Zbl 1332.42007, MR 3441105, 10.1515/forum-2014-0058; reference:[7] Duoandikoetxea, J.: Weighted norm inequalities for homogeneous singular integrals.Trans. Am. Math. Soc. 336 (1993), 869-880. Zbl 0770.42011, MR 1089418, 10.2307/2154381; reference:[8] Duoandikoetxea, J.: Sharp $L^p$ boundedness for a class of square functions.Rev. Mat. Complut. 26 (2013), 535-548. Zbl 1334.42040, MR 3068610, 10.1007/s13163-012-0106-y; reference:[9] Duoandikoetxea, J., Francia, J. L. Rubio de: Maximal and singular integral operators via Fourier transform estimates.Invent. Math. 84 (1986), 541-561. Zbl 0568.42012, MR 0837527, 10.1007/BF01388746; reference:[10] Duoandikoetxea, J., Seijo, E.: Weighted inequalities for rough square functions through extrapolation.Stud. Math. 149 (2002), 239-252. Zbl 1015.42016, MR 1890732, 10.4064/sm149-3-2; reference:[11] Fan, D., Sato, S.: Remarks on Littlewood-Paley functions and singular integrals.J. Math. Soc. Japan 54 (2002), 565-585. Zbl 1029.42010, MR 1900957, 10.2969/jmsj/1191593909; reference:[12] Garcia-Cuerva, J., Francia, J. L. Rubio de: Weighted Norm Inequalities and Related Topics.North-Holland Mathematics Studies 116, Notas de Matemática 104, North-Holland, Amsterdam (1985). Zbl 0578.46046, MR 0807149, 10.1016/s0304-0208(08)x7154-3; reference:[13] Hörmander, L.: Estimates for translation invariant operators in $L^p$ spaces.Acta Math. 104 (1960), 93-140. Zbl 0093.11402, MR 0121655, 10.1007/BF02547187; reference:[14] Rivière, N.: Singular integrals and multiplier operators.Ark. Mat. 9 (1971), 243-278. Zbl 0244.42024, MR 0440268, 10.1007/BF02383650; reference:[15] Francia, J. L. Rubio de: Factorization theory and $A_p$ weights.Am. J. Math. 106 (1984), 533-547. Zbl 0558.42012, MR 0745140, 10.2307/2374284; reference:[16] Sato, S.: Remarks on square functions in the Littlewood-Paley theory.Bull. Aust. Math. Soc. 58 (1998), 199-211. Zbl 0914.42012, MR 1642027, 10.1017/S0004972700032172; reference:[17] Sato, S.: Estimates for Littlewood-Paley functions and extrapolation.Integral Equations Oper. Theory 62 (2008), 429-440. Zbl 1166.42009, MR 2461129, 10.1007/s00020-008-1631-4; reference:[18] Sato, S.: Estimates for singular integrals along surfaces of revolution.J. Aust. Math. Soc. 86 (2009), 413-430. Zbl 1182.42019, MR 2529333, 10.1017/S1446788708000773; reference:[19] Sato, S.: Littlewood-Paley equivalence and homogeneous Fourier multipliers.Integral Equations Oper. Theory 87 (2017), 15-44. Zbl 1364.42025, MR 3609237, 10.1007/s00020-016-2333-y; reference:[20] Stein, E. M.: Singular Integrals and Differentiability Properties of Functions.Princeton Mathematical Series 30, Princeton University Press, Princeton (1970). Zbl 0207.13501, MR 0290095, 10.1515/9781400883882; reference:[21] Stein, E. M., Wainger, S.: Problems in harmonic analysis related to curvature.Bull. Am. Math. Soc. 84 (1978), 1239-1295. Zbl 0393.42010, MR 0508453, 10.1090/S0002-9904-1978-14554-6

الاتاحة: http://hdl.handle.net/10338.dmlcz/147728

المؤلفون: Hashimoto, Daiki, Ohno, Takao, Shimomura, Tetsu

مصطلحات موضوعية: keyword:Orlicz space, keyword:Riesz potential, keyword:fractional integral, keyword:metric measure space, keyword:lower Ahlfors regular, msc:31B15, msc:46E30, msc:46E35

وصف الملف: application/pdf

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الاتاحة: http://hdl.handle.net/10338.dmlcz/147628

المؤلفون: Harjulehto, Petteri, Hästö, Peter

مصطلحات موضوعية: keyword:generalized Orlicz space, keyword:Musielak-Orlicz space, keyword:nonstandard growth, keyword:variable exponent, keyword:double phase, keyword:uniform convexity, keyword:associate space, msc:46A25, msc:46E30

وصف الملف: application/pdf

Relation: mr:MR3881892; zbl:Zbl 07031693; reference:[1] Adams, R.: Sobolev Spaces.Pure and Applied Mathematics 65, Academic Press, New York (1975). Zbl 0314.46030, MR 0450957; reference:[2] Avci, M., Pankov, A.: Multivalued elliptic operators with nonstandard growth.Adv. Nonlinear Anal. 7 (2018), 35-48. Zbl 06837817, MR 3757454, 10.1515/anona-2016-0043; reference:[3] Baroni, P., Colombo, M., Mingione, G.: Non-autonomous functionals, borderline cases and related function classes.St. Petersbg. Math. J. 27 (2016), 347-379 translation from Algebra Anal. 27 2015 6-50. Zbl 1335.49057, MR 3570955, 10.1090/spmj/1392; reference:[4] Colombo, M., Mingione, G.: Regularity for double phase variational problems.Arch. Ration. Mech. Anal. 215 (2015), 443-496. Zbl 1322.49065, MR 3294408, 10.1007/s00205-014-0785-2; reference:[5] Cruz-Uribe, D., Hästö, P.: Extrapolation and interpolation in generalized Orlicz spaces.Trans. Am. Math. Soc. 370 (2018), 4323-4349. Zbl 06853979, MR 3811530, 10.1090/tran/7155; reference:[6] Diening, L., Harjulehto, P., Hästö, P., Růžička, M.: Lebesgue and Sobolev Spaces with Variable Exponents.Lecture Notes in Mathematics 2017, Springer, Berlin (2011). Zbl 1222.46002, MR 2790542, 10.1007/978-3-642-18363-8; reference:[7] Fan, X.-L., Guan, C.-X.: Uniform convexity of Musielak-Orlicz-Sobolev spaces and applications.Nonlinear Anal., Theory Methods Appl., Ser. A 73 (2010), 163-175. Zbl 1198.46010, MR 2645841, 10.1016/j.na.2010.03.010; reference:[8] Gwiazda, P., Wittbold, P., Wróblewska-Kamińska, A., Zimmermann, A.: Renormalized solutions to nonlinear parabolic problems in generalized Musielak-Orlicz spaces.Nonlinear Anal., Theory Methods Appl., Ser. A 129 (2015), 1-36. Zbl 1331.35173, MR 3414919, 10.1016/j.na.2015.08.017; reference:[9] Harjulehto, P., Hästö, P.: Riesz potential in generalized Orlicz spaces.Forum Math. 29 (2017), 229-244. MR 3592600, 10.1515/forum-2015-0239; reference:[10] Harjulehto, P., Hästö, P., Klén, R.: Generalized Orlicz spaces and related PDE.Nonlinear Anal., Theory Methods Appl., Ser. A 143 (2016), 155-173. Zbl 1360.46029, MR 3516828, 10.1016/j.na.2016.05.002; reference:[11] Harjulehto, P., Hästö, P., Toivanen, O.: Hölder regularity of quasiminimizers under generalized growth conditions.Calc. Var. Partial Differ. Equ. 56 (2017), Article No. 2, 26 pages. Zbl 1366.35036, MR 3606780, 10.1007/s00526-017-1114-z; reference:[12] Hästö, P.: The maximal operator on generalized Orlicz spaces.J. Funct. Anal. 269 (2015), 4038-4048. Zbl 1338.47032, MR 3418078, 10.1016/j.jfa.2015.10.002; reference:[13] Hudzik, H.: Uniform convexity of Musielak-Orlicz spaces with Luxemburg's norm.Ann. Soc. Math. Pol., Ser. I, Commentat. Math. 23 (1983), 21-32. Zbl 0595.46027, MR 0709167; reference:[14] Hudzik, H.: A criterion of uniform convexity of Musielak-Orlicz spaces with Luxemburg norm.Bull. Pol. Acad. Sci., Math. 32 (1984), 303-313. Zbl 0565.46020, MR 0785989; reference:[15] Maeda, F.-Y., Mizuta, Y., Ohno, T., Shimomura, T.: Boundedness of maximal operators and Sobolev's inequality on Musielak-Orlicz-Morrey spaces.Bull. Sci. Math. 137 (2013), 76-96. Zbl 1267.46045, MR 3007101, 10.1016/j.bulsci.2012.03.008; reference:[16] Musielak, J.: Orlicz Spaces and Modular Spaces.Lecture Notes in Mathematics 1034, Springer, Berlin (1983). Zbl 0557.46020, MR 0724434, 10.1007/BFb0072210; reference:[17] Ok, J.: Gradient estimates for elliptic equations with $L^{p(\cdot)}\log L$ growth.Calc. Var. Partial Differ. Equ. 55 (2016), Article No. 26, 30 pages. Zbl 1342.35090, MR 3465442, 10.1007/s00526-016-0965-z; reference:[18] Rao, M. M., Ren, Z. D.: Theory of Orlicz Spaces.Pure and Applied Mathematics 146, Marcel Dekker, New York (1991). Zbl 0724.46032, MR 1113700

الاتاحة: http://hdl.handle.net/10338.dmlcz/147517

المؤلفون: Kakizawa, Ryôhei

مصطلحات موضوعية: keyword:Helmholtz decomposition, keyword:Muckenhoupt $A_{p}$-weighted $L^{p}$-spaces, keyword:variational estimate, msc:35Q30, msc:46E30, msc:76D05

وصف الملف: application/pdf

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الاتاحة: http://hdl.handle.net/10338.dmlcz/147367

المؤلفون: Gogatishvili, Amiran, Mustafayev, Rza, Ünver, Tuğçe

مصطلحات موضوعية: keyword:Cesàro and Copson function spaces, keyword:embedding, keyword:iterated Hardy inequalities, msc:26D10, msc:46E30

وصف الملف: application/pdf

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الاتاحة: http://hdl.handle.net/10338.dmlcz/146970