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

Abstract

In this paper, generalised weighted Lp-Hardy, Lp-Caffarelli–Kohn–Nirenberg, and Lp-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 L2-Rellich type inequality with the boundary term is obtained.