Some notes on commutators of the fractional maximal and Riesz potential operators on Orlicz spaces

TL;DR

This paper investigates the boundedness of commutators of fractional maximal functions and Riesz potentials on Orlicz spaces, providing less restrictive conditions than previous results.

Contribution

It introduces new, less restrictive conditions for the boundedness of these commutators on Orlicz spaces, advancing theoretical understanding.

Findings

Established boundedness conditions for commutators on Orlicz spaces

Reduced restrictions compared to prior results

Enhanced theoretical framework for fractional operators

Abstract

The main focus of this paper is commutators and maximal commutators on Orlicz spaces for fractional maximal functions and Riesz potential. The main advance in comparison with the existing results is that we manage to obtain conditions for the boundedness in less restrictive terms.