Article
| Title: | Maximal and Riesz potential operators on Musielak-Orlicz spaces over unbounded metric measure spaces (English) |
| Author: | Ohno, Takao |
| Author: | Shimomura, Tetsu |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 75 |
| Issue: | 3 |
| Year: | 2025 |
| Pages: | 963-992 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We are concerned with the boundedness of modified Hardy-Littlewood maximal operator $M_{\lambda }$ and Sobolev inequalities for the variable Riesz potentials $I_{\alpha (\cdot ),\tau }f$ on Musielak-Orlicz spaces $L^{\Phi }(X)$ over unbounded metric measure spaces, as an improvement of our recent paper, see T. Ohno, T. Shimomura (2025a). As an application, we give the boundedness of $M_{\lambda }$ and Sobolev inequalities for $I_{\alpha (\cdot ),\tau }f$ for the multi-phase functionals with variable exponents $$ \Phi (x,t) = t^{p(x)} + a(x) t^{q(x)}+ b(x) t^{s(x)}, \quad x \in X, \ t \ge 0 , $$ where $p({\cdot })$, $q({\cdot })$, and $s({\cdot })$ are log-Hölder continuous, $p(x)<q(x) \le s(x)$ for $x\in X$, and $a({\cdot })$, and $b({\cdot })$ are nonnegative, bounded, and Hölder continuous. (English) |
| Keyword: | maximal function |
| Keyword: | Riesz potential |
| Keyword: | Musielak-Orlicz space |
| Keyword: | Sobolev's inequality |
| Keyword: | metric measure space |
| Keyword: | non-doubling measure |
| Keyword: | multi-phase functional |
| MSC: | 46E30 |
| MSC: | 46E35 |
| DOI: | 10.21136/CMJ.2025.0526-24 |
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| Date available: | 2025-09-19T12:02:40Z |
| Last updated: | 2025-09-22 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153062 |
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