New weighted Riesz-type pointwise inequalities and applications to generalized Sobolev estimates

TL;DR

This paper introduces new weighted Riesz-type inequalities that connect singular integrals, maximal functions, and Morrey spaces, leading to novel weighted Sobolev inequalities with potential applications in analysis.

Contribution

It develops a new class of weighted Riesz-type pointwise inequalities and derives associated weighted Sobolev estimates, advancing the understanding of weighted inequalities in harmonic analysis.

Findings

Established new pointwise inequalities between singular integrals and maximal functions.

Derived weighted Sobolev-type inequalities from these inequalities.

Provided potential applications to generalized Sobolev estimates.

Abstract

In this article we study some new pointwise inequalities between rough singular integral operators, weighted maximal functions of the gradient and weighted Morrey spaces. These pointwise estimates will naturally lead us to a new class of weighted Sobolev-type inequalities.