Weighted Lp‑Hardy and Lp‑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.