Commutators of Maximal Operators on Weighted Morrey Spaces

TL;DR

This paper characterizes BMO spaces via commutators of maximal functions on weighted Morrey spaces within spaces of homogeneous type, expanding understanding of these operators in complex function spaces.

Contribution

It provides a new characterization of BMO spaces through commutators of various maximal functions on weighted Morrey spaces in a general setting.

Findings

Characterization of BMO spaces using commutators of maximal functions

Extension of maximal operator theory to weighted Morrey spaces

Application within spaces of homogeneous type

Abstract

In this article we obtain the characterization for the commutators of maximal functions on the weighted Morrey spaces in the setting of spaces of homogeneous type. More precisely, we characterize BMO spaces using the commutators of Hardy-Littlewood maximal function, sharp and fractional maximal functions.