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1Academic Journal
المؤلفون: Bhairat, Sandeep P., Dhaigude, Dnyanoba-Bhaurao
مصطلحات موضوعية: keyword:fractional derivative, keyword:fractional integral, keyword:existence of solution, keyword:fractional differential equation, keyword:fixed point theorem, msc:26A33, msc:34A08, msc:34A12, msc:47H10
وصف الملف: application/pdf
Relation: mr:MR3974188; zbl:Zbl 07088846; reference:[1] Abbas, S., Benchohra, M., Lagreg, J.-E., Zhou, Y.: A survey on Hadamard and Hilfer fractional differential equations: Analysis and stability.Chaos Solitons Fractals 102 (2017), 47-71. Zbl 1374.34004, MR 3671994, 10.1016/j.chaos.2017.03.010; reference:[2] Agarwal, R. P., Benchohra, M., Hamani, S.: A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions.Acta. Appl. Math. 109 (2010), 973-1033. Zbl 1198.26004, MR 2596185, 10.1007/s10440-008-9356-6; reference:[3] Bagley, R. L., Torvik, P. J.: A different approach to the analysis of viscoelastically damped structures.AIAA J. 21 (1983), 741-748. Zbl 0514.73048, 10.2514/3.8142; reference:[4] Bagley, R. L., Torvik, P. J.: A theoretical basis for the application of fractional calculus to viscoelasticity.J. Rheol. 27 (1983), 201-210. Zbl 0515.76012, 10.1122/1.549724; reference:[5] Bagley, R. L., Torvik, P. J.: On the appearance of the fractional derivative in the behavior of real material.J. Appl. Mech. 51 (1984), 294-298. Zbl 1203.74022, 10.1115/1.3167615; reference:[6] Bhairat, S. P.: New approach to existence of solution of weighted Cauchy-type problem.Available at http://arxiv.org/abs/1808.03067 (2018), 10 pages.; reference:[7] Bhairat, S. P., Dhaigude, D. B.: Existence and stability of fractional differential equations involving generalized Katugampola derivative.Available at https://arxiv.org/ abs/1709.08838 (2017), 15 pages.; reference:[8] Chitalkar-Dhaigude, C. D., Bhairat, S. P., Dhaigude, D. B.: Solution of fractional differential equations involving Hilfer fractional derivative: Method of successive approximations.Bull. Marathwada Math. Soc. 18 (2017), 1-13.; reference:[9] Dhaigude, D. B., Bhairat, S. P.: Existence and continuation of solutions of Hilfer fractional differential equations.Available at http://arxiv.org/abs/1704.02462v1 (2017), 18 pages. MR 3820828; reference:[10] Dhaigude, D. B., Bhairat, S. P.: Existence and uniqueness of solution of Cauchy-type problem for Hilfer fractional differential equations.Commun. Appl. Anal. 22 (2017), 121-134. MR 3820828; reference:[11] Dhaigude, D. B., Bhairat, S. P.: On existence and approximation of solution of nonlinear Hilfer fractional differential equations.(to appear) in Int. J. Pure Appl. Math. Available at http://arxiv.org/abs/1704.02464 (2017), 9 pages. MR 3820828; reference:[12] Dhaigude, D. B., Bhairat, S. P.: Local existence and uniqueness of solutions for Hilfer-Hadamard fractional differential problem.Nonlinear Dyn. Syst. Theory 18 (2018), 144-153. MR 3820828; reference:[13] Dhaigude, D. B., Bhairat, S. P.: Ulam stability for system of nonlinear implicit fractional differential equations.Progress in Nonlinear Dynamics and Chaos 6 (2018), 29-38. 10.22457/pindac.v6n1a4; reference:[14] Furati, K. M., Kassim, M. D., Tatar, N.-E.: Existence and uniqueness for a problem involving Hilfer fractional derivative.Comput. Math. Appl. 64 (2012), 1616-1626. Zbl 1268.34013, MR 2960788, 10.1016/j.camwa.2012.01.009; reference:[15] Furati, K. M., Tatar, N.-E.: An existence result for a nonlocal fractional differential problem.J. Fractional Calc. 26 (2004), 43-51. Zbl 1101.34001, MR 2096756; reference:[16] Gaafar, F. M.: Continuous and integrable solutions of a nonlinear Cauchy problem of fractional order with nonlocal conditions.J. Egypt. Math. Soc. 22 (2014), 341-347. Zbl 1306.34007, MR 3260773, 10.1016/j.joems.2013.12.008; reference:[17] Hilfer, R.: Applications of Fractional Calculus in Physics.World Scientific, London (2000). Zbl 0998.26002, MR 1890104, 10.1142/9789812817747; reference:[18] Hilfer, R.: Experimental evidence for fractional time evolution in glass forming materials.Chemical Physics 284 (2002), 399-408. MR 1890106, 10.1016/S0301-0104(02)00670-5; reference:[19] Kassim, M. D., Tatar, N.-E.: Well-posedness and stability for a differential problem with Hilfer-Hadamard fractional derivative.Abstr. Appl. Anal. 2013 (2013), Article ID 605029, 12 pages. MR 3139483, 10.1155/2013/605029; reference:[20] Katugampola, U. N.: New approach to a generalized fractional integral.Appl. Math. Comput. 218 (2011), 860-865. Zbl 1231.26008, MR 2831322, 10.1016/j.amc.2011.03.062; reference:[21] Katugampola, U. N.: A new approach to generalized fractional derivatives.Bull. Math. Anal. Appl. 6 (2014), 1-15. Zbl 1317.26008, MR 3298307; reference:[22] Katugampola, U. N.: Existence and uniqueness results for a class of generalized fractional differenital equations.Available at https://arxiv.org/abs/1411.5229 (2016).; reference:[23] Kilbas, A. A., Srivastava, H. M., Trujillo, J. J.: Theory and Applications of Fractional Differential Equations.North-Holland Mathematics Studies 204. Elsevier, Amsterdam (2006). 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D.: Hilfer-Hadamard-type fractional differential equation with Cauchy-type problem.Available at https://arxiv.org/abs/1802.07483 (2018), 18 pages.; reference:[28] Wang, J., Zhang, Y.: Nonlocal initial value problems for differential equations with Hilfer fractional derivative.Appl. Math. Comput. 266 (2015), 850-859. MR 3377602, 10.1016/j.amc.2015.05.144
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2Academic Journal
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
Relation: mr:MR3923585; zbl:Zbl 07088780; reference:[1] 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:[2] Cianchi, A.: Strong and weak type inequalities for some classical operators in Orlicz spaces.J. Lond. Math. Soc., II. Ser. 60 (1999), 187-202. Zbl 0940.46015, MR 1721824, 10.1112/S0024610799007711; reference:[3] DeJarnette, N.: Is an Orlicz-Poincaré inequality an open ended condition, and what does that mean?.J. Math. Anal. Appl. 423 (2015), 358-376. Zbl 1333.46034, MR 3273185, 10.1016/j.jmaa.2014.09.064; reference:[4] Dyda, B.: Embedding theorems for Lipschitz and Lorentz spaces on lower Ahlfors regular sets.Stud. Math. 197 (2010), 247-256. Zbl 1202.46037, MR 2607491, 10.4064/sm197-3-3; reference:[5] Eridani, Gunawan, H., Nakai, E.: On generalized fractional integral operators.Sci. Math. Jpn. 60 (2004), 539-550. 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Zbl 1363.46027, MR 3360438, 10.1007/s10587-015-0187-0; reference:[24] O'Neil, R.: Fractional integration in Orlicz spaces. I.Trans. Am. Math. Soc. 115 (1965), 300-328. Zbl 0132.09201, MR 0194881, 10.2307/1994271; reference:[25] Sawano, Y., Shimomura, T.: Sobolev embeddings for generalized Riesz potentials of functions in Morrey spaces $L^{(1,\varphi)}(G)$ over nondoubling measure spaces.J. Funct. Spaces Appl. 2013 (2013), Article ID 984259, 12 pages. Zbl 1275.46017, MR 3040574, 10.1155/2013/984259; reference:[26] Sawano, Y., Shimomura, T.: Sobolev embeddings for Riesz potentials of functions in non-doubling Morrey spaces of variable exponents.Collect. Math. 64 (2013), 313-350. Zbl 1280.31001, MR 3084400, 10.1007/s13348-013-0082-7; reference:[27] Sawano, Y., Shimomura, T.: Boundedness of the generalized fractional integral operators on generalized Morrey spaces over metric measure spaces.Z. Anal. Anwend. 36 (2017), 159-190. Zbl 1364.26012, MR 3632252, 10.4171/ZAA/1584; reference:[28] Sawano, Y., Shimomura, T.: Generalized fractional integral operators over non-doubling metric measure spaces.Integral Transforms Spec. Funct. 28 (2017), 534-546. Zbl 1372.42011, MR 3645968, 10.1080/10652469.2017.1318281; reference:[29] Tolsa, X.: BMO, $H^1$, and Calderón-Zygmund operators for nondoubling measures.Math. Ann. 319 (2001), 89-149. Zbl 0974.42014, MR 1812821, 10.1007/s002080000144
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3Academic Journal
المؤلفون: Trong, Nguyen Ngoc, Truong, Le Xuan
مصطلحات موضوعية: keyword:Morrey space, keyword:Schrödinger operator, keyword:Riesz transform, keyword:fractional integral, keyword:Calderón-Zygmund estimate, msc:42B20, msc:42B35
وصف الملف: application/pdf
Relation: mr:MR3881889; zbl:Zbl 07031690; reference:[1] Adams, D. R., Xiao, J.: Nonlinear potential analysis on Morrey spaces and their capacities.Indiana Univ. Math. J. 53 (2004), 1629-1663. Zbl 1100.31009, MR 2106339, 10.1512/iumj.2004.53.2470; reference:[2] Alvarez, J., Bagby, R. J., Kurtz, D. S., Pérez, C.: Weighted estimates for commutators of linear operators.Stud. Math. 104 (1993), 195-209. Zbl 0809.42006, MR 1211818, 10.4064/sm-104-2-195-209; reference:[3] Bongioanni, B., Harboure, E., Salinas, O.: Riesz transforms related to Schrödinger operators acting on BMO type spaces.J. Math. Anal. Appl. 357 (2009), 115-131. Zbl 1180.42013, MR 2526811, 10.1016/j.jmaa.2009.03.048; reference:[4] Bongioanni, B., Harboure, E., Salinas, O.: Classes of weights related to Schrödinger operators.J. Math. Anal. Appl. 373 (2011), 563-579. Zbl 1203.42029, MR 2720705, 10.1016/j.jmaa.2010.08.008; reference:[5] Bui, T. 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T., Xiao, J., Yan, L.: Old and new Morrey spaces with heat kernel bounds.J. Fourier Anal. Appl. 13 (2007), 87-111. Zbl 1133.42017, MR 2296729, 10.1007/s00041-006-6057-2; reference:[11] Dziubański, J., Garrigós, G., Martínez, T., Torrea, J. L., Zienkiewicz, J.: BMO spaces related to Schrödinger operators with potentials satisfying reverse Hölder inequality.Mat. Z. 249 (2005), 329-356. Zbl 1136.35018, MR 2115447, 10.1007/s00209-004-0701-9; reference:[12] Dziubański, J., Zienkiewicz, J.: $H^{p}$ spaces for Schrödinger operators.Fourier Analysis and Related Topics W. Żelazko Banach Center Publications 56, Polish Academy of Sciences, Institute of Mathematics, Warsaw (2002), 45-53. Zbl 1039.42018, MR 1971563, 10.4064/bc56-0-4; reference:[13] Feuto, J., Fofana, I., Koua, K.: Spaces of functions with integrable fractional mean on locally compact groups.Afr. Mat., Sér. III French 15 (2003), 73-91. 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4Academic Journal
المؤلفون: Idris, Mochammad, Gunawan, Hendra, Eridani, A.
مصطلحات موضوعية: keyword:Bessel-Riesz operator, keyword:fractional integral operator, keyword:generalized Morrey space, msc:26A33, msc:26D10, msc:42B20, msc:42B25
وصف الملف: application/pdf
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5Academic Journal
المؤلفون: Guerraiche, Nassim, Hamani, Samira, Henderson, Johnny
مصطلحات موضوعية: keyword:fractional differential inclusion, keyword:Hadamard-type fractional derivative, keyword:fractional integral, keyword:fixed point, keyword:convex, msc:26A33, msc:34A60
وصف الملف: application/pdf
Relation: mr:MR3610653; zbl:Zbl 06674903; reference:[1] Agarwal, R.P, Benchohra, M., Hamani, S.: A survey on existence results for boundary value problems for nonlinear fractional differential equations and inclusions.Acta Appl. Math. 109 (3) (2010), 973–1033. MR 2596185, 10.1007/s10440-008-9356-6; reference:[2] Ahmed, B., Ntouyas, S.K.: Initial value problems for hybrid Hadamard fractional equations.EJDE 2014 (161) (2014), 1–8. MR 3239404; reference:[3] Aubin, J.P., Cellina, A.: Differential Inclusions.Springer-Verlag, Berlin-Heidelberg, New York, 1984. Zbl 0538.34007, MR 0755330; reference:[4] Aubin, J.P., Frankowska, H.: Set-Valued Analysis.Birkhäuser, Boston, 1990. Zbl 0713.49021, MR 1048347; reference:[5] Benchohra, M., Djebali, S., Hamani, S.: Boundary value problems of differential inclusions with Riemann-Liouville fractional derivative.Nonlinear Oscillation 14 (1) (2011), 7–20. 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Math. Math. Sci. 2004 (2004), 697–701. Zbl 1069.34002, MR 2054178, 10.1155/S0161171204302231; reference:[29] Podlubny, I.: Fractional Differential Equations.Academic Press, San Diego, 1999. Zbl 0924.34008, MR 1658022; reference:[30] Podlubny, I.: Geometric and physical interpretation of fractional integration and fractional differentiation.Fract. Calculus Appl. Anal. 5 (2002), 367–386. Zbl 1042.26003, MR 1967839; reference:[31] Thiramanus, P., Ntouyas, S.K., Tariboon, J.: Existence and uniqueness results for Hadamard-type fractional differential equations with nonlocal fractional integral boundary conditions.Abstr. Appl. Anal. (2014), Art ID 902054, 9 pp. MR 3228094; reference:[32] Zhang, S.: Positive solutions for boundary-value problems of nonlinear fractional differential equations.EJDE (2006), no. 36, 1–12. Zbl 1096.34016, MR 2213580
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6Academic Journal
مصطلحات موضوعية: keyword:Hadamard’s fractional derivative, keyword:implicit fractional differential equations in Banach space, keyword:fractional integral, keyword:existence, keyword:Gronwall’s lemma for singular kernels, keyword:Measure of noncompactness, keyword:fixed point, msc:26A33, msc:34A08
وصف الملف: application/pdf
Relation: mr:MR3674595; zbl:Zbl 1362.34010; reference:[1] Abbas, S., Benchohra, M., N’Guérékata, G. M.: Topics in Fractional Differential Equations. Springer-Verlag, New York, 2012. Zbl 1273.35001, MR 2962045; reference:[2] Abbas, S., Benchohra, M., N’Guérékata, G. M.: Advanced Fractional Differential and Integral Equations. Nova Science Publishers, New York, 2015. Zbl 1314.34002, MR 3309582; reference:[3] Agarwal, R. P., Meehan, M., O’Regan, D.: Fixed Point Theory and Applications. Cambridge University Press, Cambridge, 2001. Zbl 0960.54027, MR 1825411, 10.1017/CBO9780511543005.008; reference:[4] Ahmad, B., Ntouyas, S. K.: A fully Hadamard type integral boundary value problem of a coupled system of fractional differential equations. Fract. Calc. Appl. Anal. 17 (2014), 348–360. Zbl 1312.34005, MR 3181059, 10.2478/s13540-014-0173-5; reference:[5] Ahmad, B., Ntouyas, S. K.: Initial value problems of fractional order Hadamard-type functional differential equations. Electron. J. Differential Equations 2015, 77 (2015), 1–9. Zbl 1320.34109, MR 3337854; reference:[6] Akhmerov, K. K., Kamenskii, M. I., Potapov, A. S., Rodkina, A. E., Sadovskii, B. N.: Measures of Noncompactness and Condensing Operators. Birkhäuser Verlag, Basel, Boston, Berlin, 1992. MR 1153247; reference:[7] Appell, J.: Implicit functions, nonlinear integral equations, and the measure of noncompactness of the superposition operator. J. Math. Anal. Appl. 83 (1981), 251–263. Zbl 0495.45007, MR 0632341, 10.1016/0022-247X(81)90261-4; reference:[8] Baleanu, D., Güvenç, Z. B., Machado, J. A. T.: New Trends in Nanotechnologiy and Fractional Calculus Applications. Springer, New York, 2010. MR 2605606; reference:[9] Banaś, J., Goebel, K.: Measures of Noncompactness in Banach Spaces. Lecture Notes in Pure and Applied Mathematics 60, Marcel Dekker, New York, 1980. MR 0591679; reference:[10] Banaś, J., Olszowy, L.: Measures of noncompactness related to monotonicity. Comment. Math. 41 (2001), 13–23. 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MR 0586861, 10.1016/0362-546X(80)90010-3; reference:[21] Nieto, J. J., Ouahab, A., Venktesh, V.: Implicit fractional differential equations via the Liouville–Caputo derivative. Mathematics 3, 2 (2015), 398–411. Zbl 1322.34012, 10.3390/math3020398; reference:[22] Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego, 1999. Zbl 0924.34008, MR 1658022; reference:[23] Sun, S., Zhao, Y., Han, Z., Li, Y.: The existence of solutions for boundary value problem of fractional hybrid differential equations. Commun. Nonlinear Sci. Numer. Simul. 17 (2012), 4961–4967. Zbl 1352.34011, MR 2960290, 10.1016/j.cnsns.2012.06.001; reference:[24] Tarasov, V. E.: Fractional Dynamics: Application of Fractional Calculus to Dynamics of particles, Fields and Media. Springer & Higher Education Press, Heidelberg & Beijing, 2010. MR 2796453; reference:[25] Yosida, K.: Functional Analysis. 6th edn., Springer-Verlag, Berlin, 1980. Zbl 0435.46002, MR 0617913; reference:[26] Zhao, Y., Sun, S., Han, Z., Li, Q.: Theory of fractional hybrid differential equations. Comput. Math. Appl. 62 (2011), 1312–1324. Zbl 1228.45017, MR 2824718, 10.1016/j.camwa.2011.03.041
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7Academic Journal
المؤلفون: Hao, Zhiwei
مصطلحات موضوعية: keyword:variable exponent, keyword:atomic decomposition, keyword:martingale Hardy space, keyword:fractional integral, msc:60G42, msc:60G46
وصف الملف: application/pdf
Relation: mr:MR3441334; zbl:Zbl 06537709; reference:[1] Chao, J.-A., Ombe, H.: Commutators on dyadic martingales.Proc. Japan Acad., Ser. A 61 (1985), 35-38. Zbl 0596.47024, MR 0798032; reference:[2] Cheung, K. L., Ho, K.-P.: Boundedness of Hardy-Littlewood maximal operator on block spaces with variable exponent.Czech. Math. J. 64 (2014), 159-171. MR 3247452, 10.1007/s10587-014-0091-z; reference:[3] Cruz-Uribe, D. V., Fiorenza, A.: Variable Lebesgue Spaces: Foundations and Harmonic Analysis.Applied and Numerical Harmonic Analysis Birkhäuser, New York (2013). Zbl 1268.46002, MR 3026953; reference:[4] Cruz-Uribe, D., Fiorenza, A., Martell, J. M., Pérez, C.: The boundedness of classical operators on variable {$L^p$} spaces.Ann. Acad. Sci. Fenn., Math. 31 (2006), 239-264. Zbl 1100.42012, MR 2210118; reference:[5] Cruz-Uribe, D., Wang, L.-A. D.: Variable Hardy spaces.Indiana Univ. Math. J. 63 (2014), 447-493. Zbl 1311.42053, MR 3233216, 10.1512/iumj.2014.63.5232; reference:[6] Diening, L.: Maximal function on generalized Lebesgue spaces {$L^{p(\cdot)}$}.Math. Inequal. Appl. 7 (2004), 245-253. Zbl 1071.42014, MR 2057643; reference:[7] Diening, L., H{ä}stö, P., Roudenko, S.: Function spaces of variable smoothness and integrability.J. Funct. Anal. 256 (2009), 1731-1768. Zbl 1179.46028, MR 2498558, 10.1016/j.jfa.2009.01.017; reference:[8] Fan, X., Zhao, D.: On the spaces {$L^{p(x)}(\Omega)$} and {$W^{m,p(x)}(\Omega)$}.J. Math. Anal. Appl. 263 (2001), 424-446. Zbl 1028.46041, MR 1866056; reference:[9] Hao, Z., Jiao, Y.: Fractional integral on martingale Hardy spaces with variable exponents.Fract. Calc. Appl. Anal. 18 (2015), 1128-1145. MR 3417085; reference:[10] Ho, K.-P.: John-Nirenberg inequalities on Lebesgue spaces with variable exponents.Taiwanese J. Math. 18 (2014), 1107-1118. MR 3245432, 10.11650/tjm.18.2014.3618; reference:[11] Jiao, Y., Peng, L., Liu, P.: Atomic decompositions of Lorentz martingale spaces and applications.J. Funct. Spaces Appl. 7 (2009), 153-166. MR 2541232, 10.1155/2009/465079; reference:[12] Jiao, Y., Wu, L., Yang, A., Yi, R.: The predual and John-Nirenberg inequalities on generalized BMO martingale spaces.(to appear) in Trans. Amer. Math. Soc (2014), arXiv:1408.4641v1 [math.FA], 20 Aug. 2014. MR 3557784; reference:[13] Jiao, Y., Xie, G., Zhou, D.: Dual spaces and John-Nirenberg inequalities of martingale Hardy-Lorentz-Karamata spaces.Q. J. Math. 66 (2015), 605-623. Zbl 1317.42021, MR 3356840, 10.1093/qmath/hav003; reference:[14] Kováčik, O., Rákosník, J.: On spaces {$L^{p(x)}$} and {$W^{k,p(x)}$}.Czech. Math. J. 41 (1991), 592-618. MR 1134951; reference:[15] Liu, P., Hou, Y.: Atomic decompositions of Banach-space-valued martingales.Sci. China, Ser. A 42 (1999), 38-47. Zbl 0928.46020, MR 1692138, 10.1007/BF02872048; reference:[16] Miyamoto, T., Nakai, E., Sadasue, G.: Martingale Orlicz-Hardy spaces.Math. Nachr. 285 (2012), 670-686. Zbl 1260.60082, MR 2902839, 10.1002/mana.201000109; reference:[17] Nakai, E., Sadasue, G.: Martingale Morrey-Campanato spaces and fractional integrals.J. Funct. Spaces Appl. 2012 (2012), Article ID 673929, 29 pages. Zbl 1254.46035, MR 2944703; reference:[18] Nakai, E., Sawano, Y.: Hardy spaces with variable exponents and generalized Campanato spaces.J. Funct. Anal. 262 (2012), 3665-3748. Zbl 1244.42012, MR 2899976, 10.1016/j.jfa.2012.01.004; reference:[19] Ohno, T., Shimomura, T.: Sobolev embeddings for Riesz potentials of functions in grand Morrey spaces of variable exponents over non-doubling measure spaces.Czech. Math. J. 64 (2014), 209-228. MR 3247456, 10.1007/s10587-014-0095-8; reference:[20] Orlicz, W.: Über konjugierte Exponentenfolgen.Stud. Math. 3 German (1931), 200-211. Zbl 0003.25203, 10.4064/sm-3-1-200-211; reference:[21] Sadasue, G.: Fractional integrals on martingale Hardy spaces for $0; reference:[22] Sawano, Y.: Atomic decompositions of Hardy spaces with variable exponents and its application to bounded linear operators.Integral Equations Oper. Theory 77 (2013), 123-148. Zbl 1293.42025, MR 3090168, 10.1007/s00020-013-2073-1; reference:[23] Weisz, F.: Martingale Hardy Spaces and Their Applications in Fourier Analysis.Lecture Notes in Mathematics 1568 Springer, Berlin (1994). Zbl 0796.60049, MR 1320508, 10.1007/BFb0073448; reference:[24] Wu, L., Hao, Z., Jiao, Y.: John-Nirenberg inequalities with variable exponents on probability spaces.Tokyo J. Math. 38 (2) (2015). MR 3448862; reference:[25] Yi, R., Wu, L., Jiao, Y.: New John-Nirenberg inequalities for martingales.Stat. Probab. Lett. 86 (2014), 68-73. Zbl 1292.60051, MR 3162719, 10.1016/j.spl.2013.12.010
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8Academic Journal
المؤلفون: Perini, Alejandra
مصطلحات موضوعية: keyword:fractional integral, keyword:maximal, keyword:one-sided Calderón-Hardy, keyword:one-sided weights spaces, msc:42B20, msc:42B35
وصف الملف: application/pdf
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9Academic Journal
المؤلفون: Pradolini, Gladis, Salinas, Oscar
مصطلحات موضوعية: keyword:weights, keyword:Orlicz spaces, keyword:$BMO$, keyword:fractional integral, msc:26A33, msc:42B25, msc:46E30, msc:46E35
وصف الملف: application/pdf
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10Academic Journal
المؤلفون: Hartzstein, Silvia I., Viviani, Beatriz E.
مصطلحات موضوعية: keyword:fractional integral operators, keyword:fractional derivative operators, keyword:spaces of homogeneous type, keyword:Besov spaces, keyword:Triebel-Lizorkin spaces, msc:26A33, msc:42B20, msc:46E35, msc:47B38
وصف الملف: application/pdf
Relation: mr:MR2045849; zbl:Zbl 1127.42305; reference:[GSV] Gatto A.E., Segovia C., Vági S.: On fractional differentiation and integration on spaces of homogeneous type.Rev. Mat. Iberoamericana 12 2 (1996), 111-145. MR 1387588; reference:[H] Hartzstein S.I.: Acotación de operadores de Calderón-Zygmund en espacios de Triebel-Lizorkin y de Besov generalizados sobre espacios de tipo homogéneo.Thesis, 2000, UNL, Santa Fe, Argentina.; reference:[HV1] Hartzstein S.I., Viviani B.E.: $T1$ theorems on generalized Besov and Triebel-Lizorkin spaces over spaces of homogeneous type.Revista de la Unión Matemática Argentina, 42 1 (2000), 51-73. Zbl 0995.42011, MR 1852730; reference:[HV2] Hartzstein S.I., Viviani B.E.: Integral and derivative operators of functional order on generalized Besov and Triebel-Lizorkin spaces in the setting of spaces of homogeneous type.Comment. Math. Univ. Carolinae 43 (2002), 723-754. Zbl 1091.26002, MR 2046192; reference:[MS] Macías R.A., Segovia C.: Lipschitz functions on spaces of homogeneous type.Adv. in Math. 33 (1979), 257-270. MR 0546295
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11Academic Journal
المؤلفون: Hartzstein, Silvia I., Viviani, Beatriz E.
مصطلحات موضوعية: keyword:integral and derivative operators of functional order, keyword:fractional integral operator, keyword:fractional derivative operator, keyword:spaces of homogeneous type, keyword:Besov spaces, keyword:Triebel-Lizorkin spaces, msc:26A33, msc:42B35, msc:46E35, msc:47G10
وصف الملف: application/pdf
Relation: mr:MR2046192; zbl:Zbl 1091.26002; reference:[B] Blasco O.: Weighted Lipschitz spaces defined by a Banach space.García-Cuerva, J. et al., Fourier Analysis and Partial Differential Equations, CRC, 1995, Chapter 7, pp.131-140. Zbl 0870.46021, MR 1330235; reference:[FJW] Frazier M., Jawerth B., Weiss G.: Littlewood-Paley theory and the study of function spaces.CBMS, Regional Conference Series in Math., No. 79, 1991. Zbl 0757.42006, MR 1107300; reference:[GSV] Gatto A.E., Segovia C., Vági S.: On fractional differentiation and integration on spaces of homogeneous type.Rev. Mat. Iberoamericana 12 2 (1996), 111-145. MR 1387588; reference:[GV] Gatto A.E., Vági S.: On Sobolev spaces of fractional order and $\epsilon$-families of operators on spaces of homogeneous type.Studia Math. 133.1 (1999), 19-27. MR 1671965; reference:[H] Hartzstein S.I. Acotación de operadores de Calderón-Zygmund en espacios de Triebel-Lizorkin y de Besov generalizados sobre espacios de tipo homogéneo: Thesis, 2000, UNL, Santa Fe, Argentina.; reference:[HV] Hartzstein S.I., Viviani B.E.: $T1$ theorems on generalized Besov and Triebel-Lizorkin spaces over spaces of homogeneous type.Revista de la Unión Matemática Argentina 42 1 (2000), 51-73. Zbl 0995.42011, MR 1852730; reference:[HS] Han Y.-S., Sawyer E.T.: Littlewood-Paley theory on spaces of homogeneous type and the classical function spaces.Memoirs Amer. Math. Soc., Vol. 110, No .530, 1994. Zbl 0806.42013, MR 1214968; reference:[I] Iaffei B.: Espacios Lipschitz generalizados y operadores invariantes por traslaciones.Thesis, UNL, 1996.; reference:[J] Janson S.: Generalization on Lipschitz spaces and applications to Hardy spaces and bounded mean oscillation.Duke Math. J. 47 (1980), 959-982. MR 0596123; reference:[MS] Macías R.A., Segovia C.: Lipschitz functions on spaces of homogeneous type.Adv. Math. 33 (1979), 257-270. MR 0546295
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12Academic Journal
المؤلفون: Pradolini, Gladis
مصطلحات موضوعية: keyword:two-weighted inequalities, keyword:fractional integral, keyword:weighted Lebesgue spaces, keyword:\newline weighted Lipschitz spaces, keyword:weighted BMO spaces, msc:42B25, msc:47B38, msc:47G10
وصف الملف: application/pdf
Relation: mr:MR1825378; zbl:Zbl 1055.42015; reference:[CF] Coifman R., Fefferman C.: Weighted norm inequalities for maximal functions and singular integrals.Studia Math. 51 (1974), 241-250. Zbl 0291.44007, MR 0358205; reference:[HL] Hardy G., Littlewood J.: Some properties of fractional integrals.Math. Z. 27 (1928), 565-606. MR 1544927; reference:[HSV] Harboure E., Salinas O., Viviani B.: Boundedness of the fractional integral on weighted Lebesgue and Lipschitz spaces.Trans. Amer. Math. Soc. 349 (1997), 235-255. Zbl 0865.42017, MR 1357395; reference:[MW1] Muckenhoupt B., Wheeden R.: Weighted norm inequalities for fractional integral.Trans. Amer. Math. Soc. 192 (1974), 261-274. MR 0340523; reference:[MW2] Muckenhoupt B., Wheeden R.: Weighted bounded mean oscillation and Hilbert transform.Studia Math. T. LIV, pp.221-237, 1976. MR 0399741; reference:[Pe] Peetre, J.: On the theory of ${\Cal L}_{p,\lambda }$ spaces.J. Funct. Anal. 4 (1969), 71-87.; reference:[P] Pradolini G.: Two-weighted norm inequalities for the fractional integral operator between $L^p$ and Lipschitz spaces.to appear in Comment. Math. Polish Acad. Sci. MR 1876717; reference:[S] Sobolev S.L.: On a theorem in functional analysis.Math. Sb. 4 (46) (1938), 471-497; English transl.: Amer. Math. Soc. Transl. (2) 34 (1963), 39-68.; reference:[SWe] Stein E., Weiss G.: Fractional integrals on n-dimensional euclidean space.J. Math. Mech. 7 (1958), 503-514; MR 20#4746. Zbl 0082.27201, MR 0098285; reference:[WZ] Wheeden R., Zygmund A.: Measure and Integral. An Introduction to Real Analysis.Marcel Dekker Inc, 1977. Zbl 0362.26004, MR 0492146