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arXiv · 2307.15500

Commutators of the maximal and sharp functions with weighted Lipschitz functions

Pu Zhang·Xiaomeng Zhu
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Abstract

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.

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Pu Zhang, Xiaomeng Zhu. 2023-07-28. Commutators of the maximal and sharp functions with weighted Lipschitz functions. https://arxiv.org/abs/2307.15500

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