A homage to Guido Weiss and his leadership of the Saint Louis team: Commutators of Singular Integrals and Sobolev inequalities

TL;DR

This paper extends classical Sobolev inequalities to include linear and non-linear commutators, enhancing understanding of their mathematical properties and applications.

Contribution

It introduces new Sobolev-type inequalities for commutators, broadening the scope of existing theoretical frameworks.

Findings

Extended Sobolev inequalities for commutators

Improved bounds for linear and non-linear cases

Enhanced theoretical understanding of commutator behavior

Abstract

We extend some classical Sobolev-type inequalities for linear and non-linear commutators.