Boundedness of the Hardy-Littlewood Maximal Operator, Fractional Integral Operators, and Calderon-Zygmund Operators on Generalized Weighted Morrey Spaces

TL;DR

This paper establishes the boundedness of key classical operators such as the Hardy-Littlewood maximal operator, fractional integral, and Calderon-Zygmund operators on generalized weighted Morrey spaces, broadening understanding of their behavior in these contexts.

Contribution

The paper proves the boundedness of these operators on generalized weighted Morrey spaces and weak Morrey spaces under specific conditions, extending previous results to more general settings.

Findings

Operators are bounded on generalized weighted Morrey spaces.

Boundedness holds under certain assumptions on weights.

Results extend classical boundedness to broader function spaces.

Abstract

In this paper we investigate the boundedness of classical operators, namely the Hardy-Littlewood maximal operator, fractional integral operators, and Calderon-Zygmund operators, on generalized weighted Morrey spaces and generalized weighted weak Morrey spaces. We prove that the operators are bounded on these spaces, under certain assumptions.