Article
| Title: | Weighted Hardy-Sobolev type integrability for generalized Riesz potentials in weighted Morrey-Orlicz spaces (English) |
| Author: | Mizuta, Yoshihiro |
| Author: | Shimomura, Tetsu |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 75 |
| Issue: | 4 |
| Year: | 2025 |
| Pages: | 1177-1195 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We are concerned with weighted Hardy-Sobolev type integrabilities for generalized Riesz potentials $$ R_{\alpha ,m}f(x) = \int _{{\mathbb R}^n} R_{\alpha ,m} (x,y) f(y) {\rm d} y $$ of functions $f$ in weighted Morrey-Orlicz spaces, where $R_{\alpha }(x) = |x|^{\alpha -n}$ and $$ R_{\alpha ,m}(x,y) = R_{\alpha }(x-y) - \sum _{|\ell | \le m-1} \frac {y^{\ell }}{\ell !} (D^{\ell }R_{\alpha })(-x). $$ Those potentials are used to give a representation of $C^1$-functions on the punctured space ${\mathbb R} ^n\setminus \{0\}$. As an application, we obtain Hardy-Sobolev type integrabilities for general double phase functionals given by $$ \varphi (x,t) =\varphi _1(t) + \varphi _2(b(x)t). $$ (English) |
| Keyword: | Hardy-Sobolev integrability |
| Keyword: | generalized Riesz potential |
| Keyword: | weighted Morrey-Orlicz space |
| Keyword: | double phase functional |
| MSC: | 26D15 |
| MSC: | 46E30 |
| MSC: | 47G10 |
| DOI: | 10.21136/CMJ.2025.0533-24 |
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| Date available: | 2025-12-20T07:15:35Z |
| Last updated: | 2025-12-22 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153236 |
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