Commutators of integral operators with functions in Campanato spaces on Orlicz-Morrey spaces

TL;DR

This paper investigates the boundedness of commutators involving Calderón-Zygmund and fractional integral operators with functions in Campanato spaces on Orlicz-Morrey spaces, establishing necessary and sufficient conditions.

Contribution

It introduces Orlicz-Campanato spaces, proves boundedness of generalized fractional maximal operators, and characterizes commutator boundedness on Orlicz-Morrey spaces.

Findings

Necessary and sufficient conditions for commutator boundedness.

Boundedness of generalized fractional maximal operators.

Introduction of Orlicz-Campanato spaces and their relations.

Abstract

We consider the commutators $[b,T]$ and $[b,I_{\rho}]$ on Orlicz-Morrey spaces, where $T$ is a Calder\'on-Zygmund operator, $I_{\rho}$ is a generalized fractional integral operator and $b$ is a function in generalized Campanato spaces. We give a necessary and sufficient condition for the boundedness of the commutators on Orlicz-Morrey spaces. To do this we prove the boundedness of generalized fractional maximal operators on Orlicz-Morrey spaces. Moreover, we introduce Orlicz-Campanato spaces and establish their relations to Orlicz-Morrey spaces.