Commutators of the maximal and sharp functions with weighted Lipschitz functions
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913195279515648 |
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| author | Zhang, Pu Zhu, Xiaomeng |
| author_facet | Zhang, Pu Zhu, Xiaomeng |
| contents | Let $M$ be the Hardy-Littlewood maximal function. Denote by $M_b$ and $[b,M]$ the maximal and the nonlinear commutators of $M$ with a function $b$. The boundedness of $M_b$ and $[b,M]$ on weighted Lebesgue spaces are characterized when the symbols $b$ belong to weighted Lipschitz (weighted Morrey-Campanato) spaces. Some new characterizations for weighted Lipschitz spaces are obtained. Similar results are also established for the nonlinear commutator of the sharp function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_15500 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Commutators of the maximal and sharp functions with weighted Lipschitz functions Zhang, Pu Zhu, Xiaomeng Classical Analysis and ODEs Analysis of PDEs Functional Analysis 42B25, 42B20, 26A16, 47B47 Let $M$ be the Hardy-Littlewood maximal function. Denote by $M_b$ and $[b,M]$ the maximal and the nonlinear commutators of $M$ with a function $b$. The boundedness of $M_b$ and $[b,M]$ on weighted Lebesgue spaces are characterized when the symbols $b$ belong to weighted Lipschitz (weighted Morrey-Campanato) spaces. Some new characterizations for weighted Lipschitz spaces are obtained. Similar results are also established for the nonlinear commutator of the sharp function. |
| title | Commutators of the maximal and sharp functions with weighted Lipschitz functions |
| topic | Classical Analysis and ODEs Analysis of PDEs Functional Analysis 42B25, 42B20, 26A16, 47B47 |
| url | https://arxiv.org/abs/2307.15500 |