Article
| Title: | Weighted norm inequalities for vector-valued convolution operators via capacity (English) |
| Author: | Han, Yaoyao |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 76 |
| Issue: | 3 |
| Year: | 2026 |
| Pages: | 849-877 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | This paper is devoted to the study of a class of vector-valued convolution operators. A fundamental problem in this context is to characterize the nonnegative measures $\mu $ for which such operators are bounded from $L^p(\ell ^1)$ to $L^q(\ell ^1; \mu )$. Inspired by classical capacity theory, we introduce a novel notion of $L^p(\ell ^1)$ capacity specifically adapted to the vector-valued setting. By developing this capacity approach, we establish complete necessary and sufficient conditions on the measure $\mu $ for the boundedness of the operators. Our results provide a unified characterization that covers both cases $p \leq q$ and $q < p$. The findings yield a powerful tool for analyzing mapping properties of vector-valued operators in weighted spaces. (English) |
| Keyword: | vector-valued space |
| Keyword: | $L^p(\ell ^1)$ capacity |
| Keyword: | vector-valued extension |
| Keyword: | boundedness |
| MSC: | 26D15 |
| MSC: | 31C15 |
| DOI: | 10.21136/CMJ.2026.0396-25 |
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| Date available: | 2026-09-11T13:12:46Z |
| Last updated: | 2026-09-14 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153731 |
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