Two-Weighted Inequalities for Hardy-Littlewood Maximal Functions and Singular Integrals in $l^{p(\cdot)}$ Spaces

TL;DR

This paper establishes two-weight criteria for the Hardy-Littlewood maximal operator and singular integrals within variable exponent Lebesgue spaces on the real line, advancing the understanding of weighted inequalities in these spaces.

Contribution

It introduces new two-weight criteria for maximal functions and singular integrals in variable exponent Lebesgue spaces, expanding the theoretical framework for weighted inequalities.

Findings

Derived new two-weight inequalities for maximal functions.

Established criteria for singular integrals in variable exponent spaces.

Extended classical results to variable exponent settings.

Abstract

Two-weight criteria of various type for the Hardy-Littlewood maximal operator and singular integrals in variable exponent Lebesgue spaces defined on the real line are established.