Boundedness of fractional operators in weighted variable exponent spaces with non doubling measures

TL;DR

This paper establishes weighted norm inequalities for fractional operators in variable exponent Lebesgue spaces with non-doubling measures, expanding understanding of their boundedness properties in complex measure spaces.

Contribution

It provides new boundedness results for fractional maximal and integral operators in variable exponent spaces with non-doubling measures, a less explored area.

Findings

Weighted norm inequalities are proven for fractional operators.

Results apply to spaces with non-doubling measures.

The work extends classical results to more general measure spaces.

Abstract

In the context of variable exponent Lebesgue spaces equipped with a lower Ahlfors measure we obtain weighted norm inequalities over bounded domains for the centered fractional maximal function and the fractional integral operator.