Weighted $L^p$-Hardy and $L^p$-Rellich inequalities with boundary terms on stratified Lie groups

TL;DR

This paper establishes generalized weighted $L^p$-Hardy, $L^p$-Rellich, and related inequalities with boundary terms on stratified Lie groups, extending classical results and deriving uncertainty principles.

Contribution

It introduces new weighted inequalities with boundary terms on stratified Lie groups, broadening the scope of Hardy and Rellich inequalities in this setting.

Findings

Derived generalized weighted $L^p$-Hardy inequalities with boundary terms.

Revealed new $L^p$-Rellich inequalities with boundary terms.

Recovered classical Hardy and uncertainty principles on stratified groups.

Abstract

In this paper, generalised weighted $L^p$-Hardy,$ L^p$-Caffarelli-Kohn-Nirenberg, and $L^p$-Rellich inequalities with boundary terms are obtained on stratified Lie groups. As consequences, most of the Hardy type inequalities and Heisenberg- Pauli-Weyl type uncertainty principles on stratified groups are recovered. Moreover, a weighted $L^2$-Rellich type inequality with the boundary term is obtained.