Endpoint estimates for commutators with respect to the fractional integral operators on Orlicz-Morrey spaces

TL;DR

This paper extends the understanding of endpoint estimates for commutators of fractional integral operators, demonstrating their weak-type boundedness on Orlicz-Morrey spaces, building on prior results in Morrey and Orlicz spaces.

Contribution

It introduces the weak-type boundedness of commutators on Orlicz-Morrey spaces, expanding previous endpoint estimates to this more general setting.

Findings

Established weak-type boundedness of commutators on Orlicz-Morrey spaces.

Extended previous results from Morrey and Orlicz spaces.

Provided new endpoint estimates for fractional integral operators.

Abstract

It is known that the necessary and sufficient conditions of the boundedness of commutators on Morrey spaces are given by Di Fazio, Ragusa and Shirai. Moreover, according to the result of Cruz-Uribe and Fiorenza in 2003, it is given that the weak-type boundedness of the commutators of the fractional integral operators on the Orlicz spaces as the endpoint estimates. In this paper, we gave the extention to the weak-type boundedness on the Orlicz-Morrey spaces.