带加权Lipschitz函数的极大函数和锐函数的对易子

arXiv (Cornell University) Pub Date : 2023-07-28 DOI:10.48550/arxiv.2307.15500

Zhang, Pu, Zhu, Xiaomeng

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引用次数: 0

摘要

设M为Hardy-Littlewood极大函数。用$M_b$和$[b,M]$表示$M$与函数$b$的极大值和非线性对易子。当符号$b$属于加权Lipschitz空间时，刻画了$M_b$和$[b,M]$在加权Lebesgue空间上的有界性。得到了加权Lipschitz空间的一些新的表征。对于夏普函数的非线性换向器也得到了类似的结果。

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Commutators of the maximal and sharp functions with weighted Lipschitz functions

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 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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arXiv (Cornell University)

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