A note on precised Hardy inequalities on Carnot groups and Riemannian manifolds

TL;DR

This paper establishes non-local Hardy inequalities on Carnot groups and Riemannian manifolds using integral representations of fractional Sobolev norms, expanding the understanding of Hardy inequalities in geometric analysis.

Contribution

It introduces new non-local Hardy inequalities applicable to Carnot groups and Riemannian manifolds, utilizing fractional Sobolev norm representations.

Findings

Proved non-local Hardy inequalities on Carnot groups.

Extended Hardy inequalities to Riemannian manifolds.

Utilized integral representations of fractional Sobolev norms.

Abstract

We prove non local Hardy inequalities on Carnot groups and Riemannian manifolds, relying on integral representations of fractional Sobolev norms.