Characterizations of Sobolev inequalities on metric spaces

TL;DR

This paper provides a broad characterization of Sobolev inequalities in metric measure spaces using isocapacitary methods, extending their understanding in general metric settings.

Contribution

It introduces isocapacitary characterizations of Sobolev inequalities applicable to very general metric measure spaces, broadening the theoretical framework.

Findings

Isocapacitary characterizations of Sobolev inequalities established

Applicable to a wide class of metric measure spaces

Enhances understanding of Sobolev inequalities in abstract metric settings

Abstract

We present isocapacitary characterizations of Sobolev inequalities in very general metric measure spaces.