A characterization for fractional integral and its commutators in Orlicz and generalized Orlicz-Morrey spaces on spaces of homogeneous type

TL;DR

This paper studies the boundedness of fractional integrals and their commutators in generalized Orlicz-Morrey and Orlicz spaces on spaces of homogeneous type, providing necessary and sufficient conditions.

Contribution

It establishes new criteria for the boundedness of fractional integrals and commutators in these advanced function spaces, extending previous results to more general settings.

Findings

Derived necessary and sufficient conditions for boundedness

Established Adams type boundedness results

Analyzed criteria in Orlicz and generalized Orlicz-Morrey spaces

Abstract

In this paper, we investigate the boundedness of maximal operator and its commutators in generalized Orlicz-Morrey spaces on the spaces of homogeneous type. As an application of this boundedness, we give necessary and sufficient condition for the Adams type boundedness of fractional integral and its commutators in these spaces. We also discuss criteria for the boundedness of these operators in Orlicz spaces.