Calder\'{o}n-Zygmund operators and their commutators on generalized weighted Orlicz-Morrey spaces

TL;DR

This paper establishes conditions for the boundedness of Calderón-Zygmund operators and their commutators on generalized weighted Orlicz-Morrey spaces, including vector-valued cases, advancing harmonic analysis in these complex function spaces.

Contribution

It provides necessary and sufficient criteria for boundedness of Calderón-Zygmund operators and their commutators on generalized weighted Orlicz-Morrey spaces, including vector-valued extensions.

Findings

Characterization of weak/strong boundedness conditions

Boundedness results for commutators of Calderón-Zygmund operators

Vector-valued boundedness of Calderón-Zygmund operators

Abstract

In this paper, we obtain the necessary and sufficient conditions for the weak/strong boundedness of the Calder\'{o}n-Zygmund operators in generalized weighted Orlicz-Morrey spaces. We also study the boundedness of the commutators of Calder\'{o}n-Zygmund operators on these spaces. Moreover, the boundedness of Calder\'{o}n-Zygmund operators in the vector-valued setting is given.