The boundedness of certain sublinear operators with rough kernel generated by Calder\'on-Zygmund operators and their commutators on generalized weighted Morrey spaces

TL;DR

This paper establishes the boundedness of certain sublinear operators with rough kernels and their commutators on generalized weighted Morrey spaces, broadening understanding of harmonic analysis operators.

Contribution

It proves boundedness results for sublinear operators with rough kernels and their commutators on generalized weighted Morrey spaces, including Marcinkiewicz operators.

Findings

Boundedness of sublinear rough kernel operators on generalized weighted Morrey spaces.

Boundedness of commutators with BMO functions on these spaces.

Application to Marcinkiewicz operators.

Abstract

The aim of this paper is to get the boundedness of certain sublinear operators with rough kernel generated by Calder\'on-Zygmund operators on the generalized weighted Morrey spaces under generic size conditions which are satisfied by most of the operators in harmonic analysis. We also prove that the commutator operators formed by BMO functions and certain sublinear operators with rough kernel are also bounded on the generalized weighted Morrey spaces. Marcinkiewicz operator which satisfies the conditions of these theorems can be considered as an example.