Two weighted estimates for generalized fractional maximal operators on non homogeneous spaces

TL;DR

This paper investigates weighted bounds for generalized fractional maximal operators on non-homogeneous spaces with measures that are not necessarily doubling, providing improved two-weight inequalities relevant for commutators of singular and fractional operators.

Contribution

It introduces new weighted estimates for fractional maximal operators in non-homogeneous spaces, extending and improving previous two-weight results.

Findings

Established new boundedness criteria for fractional maximal operators

Improved two-weight inequalities for specific fractional maximal operators

Linked maximal operators with commutators of singular and fractional operators

Abstract

Let $\mu$ be a non-negative Borel measure on $R^d$ satisfying that the measure of a cube in $R^d$ is smaller than the length of its side raised to the $n$-th power, $0<n\leq d$. In this article we study the class of weights related to the boundedness of radial fractional type maximal operator associated to a Young function $B$ in the context of non-homogeneous spaces related with the measure $\mu$. This type of maximal operators are the adequate operators related with commutators of singular and fractional operators. Particularly, we give an improvement of a two weighted result for certain fractional maximal operator proved in [26].