Publication date:
7 September 2017
Source:Advances in Mathematics, Volume 317
Author(s): Michael Ruzhansky, Durvudkhan Suragan
We give sharp remainder terms of $L^p$ and weighted Hardy and Rellich inequalities on one of most general subclasses of nilpotent Lie groups, namely the class of homogeneous groups. As consequences, we obtain analogues of the generalised classical Hardy and Rellich inequalities and the uncertainty principle on homogeneous groups. We also prove higher order inequalities of Hardy–Rellich type, all with sharp constants. A number of identities are derived including weighted and higher order types.