On the Boundedness of the Maximal and Fractional Maximal, Potential Operators in the Global Morrey-Type Spaces with Variable Exponents

TL;DR

This paper investigates the boundedness of maximal and potential operators within global Morrey-type spaces that have variable exponents, extending understanding of these operators in more general, unbounded contexts.

Contribution

It establishes the boundedness of Hardy-Littlewood maximal and potential operators in global Morrey-type spaces with variable exponents, a generalization beyond classical fixed-exponent spaces.

Findings

Boundedness of maximal operators in unbounded Morrey-type spaces.

Boundedness of potential operators in these spaces.

Extension of operator theory to variable exponent, unbounded settings.

Abstract

We consider the global Morrey-type spaces with variable exponents and general function defining these spaces. In the case of unbounded sets, we prove boundedness of the Hardy-Littlewood maximal operator, potential type operator in these spaces.