Fractional maximal operators on weighted variable Lebesgue spaces over the spaces of homogeneous type

TL;DR

This paper introduces a new class of fractional-type weights on spaces of homogeneous type and characterizes the boundedness of fractional maximal operators on weighted variable Lebesgue spaces, generalizing previous results.

Contribution

It establishes a new class of fractional weights and provides weighted strong and weak-type characterizations for fractional maximal operators on these spaces.

Findings

New class of fractional weights $A_{p( abla), q( abla)}(X)$ introduced.

Weighted boundedness characterized for fractional maximal operators.

Generalizes previous results by multiple researchers.

Abstract

Let $(X,d,\mu)$ is a space of homogeneous type, we establish a new class of fractional-type variable weights $A_{p(\cdot), q(\cdot)}(X)$. Then, we get the new weighted strong-type and weak-type characterizations for fractional maximal operators $M_\eta$ on weighted variable Lebesgue spaces over $(X,d,\mu)$. This study generalizes the results by Cruz-Uribe-Fiorenza-Neugebauer (2012), Bernardis-Dalmasso-Pradolini (2014), Cruz-Uribe-Shukla (2018), and Cruz-Uribe-Cummings (2022).