Academic Journal
Boundedness properties of maximal operators on Lorentz spaces
| العنوان: | Boundedness properties of maximal operators on Lorentz spaces |
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| المؤلفون: | Kosz, Dariusz |
| المصدر: | Annales Fennici Mathematici; Vol. 48 No. 2 (2023); 515-535 ; Annales Fennici Mathematici; Vol 48 Nro 2 (2023); 515-535 ; 2737-114X ; 2737-0690 |
| بيانات النشر: | The Finnish Mathematical Society |
| سنة النشر: | 2023 |
| المجموعة: | Federation of Finnish Learned Societies: Scientific Journals Online |
| مصطلحات موضوعية: | Centered Hardy-Littlewood maximal operator, Lorentz space, nondoubling metric measure space |
| الوصف: | We study mapping properties of the centered Hardy-Littlewood maximal operator \(M\) acting on Lorentz spaces. Given \(p \in (1,\infty)\) and a metric measure space \(X = (X, \rho, \mu)\) we let \(\Omega^p_{\rm HL}(X) \subset [0,1]^2\) be the set of all pairs \((\frac{1}{q},\frac{1}{r})\) such that \(M\) is bounded from \(L^{p,q}(X)\) to \(L^{p,r}(X)\). Under mild assumptions on \(\mu\), for each fixed \(p\) all possible shapes of \(\Omega^p_{\rm HL}(X)\) are characterized. Namely, we show that the boundary of \(\Omega^p_{\rm HL}(X)\) either is empty or takes the form \(\{ \delta \} \times [0, \lim_{u \rightarrow \delta} F(u)] \cup \{(u, F(u)) \colon u \in (\delta, 1] \}\), where \(\delta \in [0,1]\) and \(F \colon [\delta, 1] \rightarrow [0,1]\) is concave, nondecreasing, and satisfies \(F(u) \leq u\). Conversely, for each such \(F\) we find \(X\) such that \(M\) is bounded from \(L^{p,q}(X)\) to \(L^{p,r}(X)\) if and only if the point \((\frac{1}{q}, \frac{1}{r})\) lies on or under the graph of \(F\), that is, \(\frac{1}{q} \geq \delta\) and \(\frac{1}{r} \leq F\big(\frac{1}{q}\big)\). |
| نوع الوثيقة: | article in journal/newspaper |
| وصف الملف: | application/pdf |
| اللغة: | English |
| Relation: | https://afm.journal.fi/article/view/131758/80521; https://afm.journal.fi/article/view/131758 |
| DOI: | 10.54330/afm.131758 |
| الاتاحة: | https://afm.journal.fi/article/view/131758 https://doi.org/10.54330/afm.131758 |
| Rights: | Copyright (c) 2023 Annales Fennici Mathematici ; https://creativecommons.org/licenses/by-nc/4.0 |
| رقم الانضمام: | edsbas.3EB90A08 |
| قاعدة البيانات: | BASE |
| DOI: | 10.54330/afm.131758 |
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