Two-Weighted Norm Inequalities for the Double Hardy Transforms and Strong Fractional Maximal Functions in Variable Exponent Lebesgue Spaces

TL;DR

This paper establishes two-weight norm inequalities for double Hardy transforms and strong fractional maximal functions within variable exponent Lebesgue spaces, providing necessary and sufficient conditions in specific cases.

Contribution

It introduces new two-weight norm estimates for these operators in variable exponent spaces, with conditions that are both necessary and sufficient when the exponent is constant.

Findings

Derived necessary and sufficient conditions for the inequalities.

Extended classical results to variable exponent Lebesgue spaces.

Provided a comprehensive framework for analyzing these operators.

Abstract

Two-weight norm estimates for the double Hardy transforms and strong fractional maximal functions are established in variable exponent Lebesgue spaces. Derived conditions are simultaneously necessary and sufficient in the case when the exponent of the right-hand side space is constant.