Maximal and Calderon-Zygmund operators on the local variable Morrey-Lorentz spaces and some applications

TL;DR

This paper introduces local variable Morrey-Lorentz spaces, proves the boundedness of key operators like Hardy Littlewood maximal and Calderon-Zygmund on these spaces, and applies these results to various classical operators.

Contribution

It defines a new class of function spaces and establishes boundedness results for important operators within these spaces, extending previous analysis.

Findings

Boundedness of Hardy Littlewood maximal operator on these spaces

Boundedness of Calderon-Zygmund operators on these spaces

Applications to Bochner Riesz, identity approximation, and Marcinkiewicz operators

Abstract

In this paper, we give the definition of local variable Morrey Lorentz spaces which are a new class of functions. Also, we prove the boundedness of the Hardy Littlewood maximal operator M and Calderon Zygmund operators T on these spaces. Finally, we apply these results to the Bochner Riesz operator, identity approximation and the Marcinkiewicz operator on these spaces.