Weighted norm inequalities for convolution and Riesz potential

TL;DR

This paper extends classical inequalities to weighted Lebesgue spaces, providing new bounds for convolution and Riesz potential operators with weights.

Contribution

It introduces weighted norm inequalities for convolution and Riesz potential operators, generalizing existing unweighted results.

Findings

Proved weighted inequalities for convolution operators.

Established two-sided weighted inequalities for Riesz potentials.

Extended classical inequalities to weighted settings.

Abstract

In this paper, we prove analogues of O'Neil's inequalities for the convolution in the weighted Lebesgue spaces. We also establish the weighted two-sided norm inequalities for the potential operator.