Commutators for the maximal and sharp functions with weighted Lipschitz functions on weighted Morrey spaces

TL;DR

This paper investigates the boundedness of commutators involving maximal functions on weighted Morrey spaces with symbols in weighted Lipschitz spaces, providing new characterizations of these functions.

Contribution

It introduces novel characterizations of weighted Lipschitz functions via the boundedness of commutators on weighted Morrey spaces.

Findings

Boundedness of commutators characterized for weighted Lipschitz symbols

New criteria for weighted Lipschitz functions based on commutator boundedness

Enhanced understanding of maximal function commutators in weighted Morrey spaces

Abstract

We study the boundedness of commutators of the Hardy-Littlewood maximal function and the sharp maximal function on weighted Morrey spaces when the symbols of the commutators belong to weighted Lipschitz spaces. Some new characterizations for weighted Lipschitz functions are obtained in term of the boundedness of the commutators.