English

Commutators of the maximal and sharp functions with weighted Lipschitz functions

Classical Analysis and ODEs 2024-01-17 v2 Analysis of PDEs Functional Analysis

Abstract

Let MM be the Hardy-Littlewood maximal function. Denote by MbM_b and [b,M][b,M] the maximal and the nonlinear commutators of MM with a function bb. The boundedness of MbM_b and [b,M][b,M] on weighted Lebesgue spaces are characterized when the symbols bb 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.

Keywords

Cite

@article{arxiv.2307.15500,
  title  = {Commutators of the maximal and sharp functions with weighted Lipschitz functions},
  author = {Pu Zhang and Xiaomeng Zhu},
  journal= {arXiv preprint arXiv:2307.15500},
  year   = {2024}
}
R2 v1 2026-06-28T11:42:48.495Z