Subelliptic geometric Hardy type inequalities on half-spaces and convex domains

TL;DR

This paper extends Hardy inequalities to stratified Lie groups like the Heisenberg and Engel groups, providing new $L^2$ and $L^p$ inequalities on half-spaces and convex domains, with applications to uncertainty principles.

Contribution

It introduces $L^2$ and $L^p$ geometric Hardy inequalities on stratified Lie groups, a novel extension in the context of half-spaces and convex domains.

Findings

Derived new Hardy inequalities for stratified Lie groups.

Established geometric uncertainty principles.

Provided explicit examples for Heisenberg and Engel groups.

Abstract

In this paper we present $L^2$ and $L^p$ versions of the geometric Hardy inequalities in half-spaces and convex domains on stratified (Lie) groups. As a consequence, we obtain the geometric uncertainty principles. We give examples of the obtained results for the Heisenberg and the Engel groups.