Commutators of the maximal and sharp functions with weighted Lipschitz functions

Pu Zhang; Xiaomeng Zhu

paper

Commutators of the maximal and sharp functions with weighted Lipschitz functions

arXiv:2307.15500

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.