Hardy and Rellich inequalities, identities, and sharp remainders on homogeneous groups

By Michael Ruzhansky, Durvudkhan Suragan. 2016

88 citations recorded by the source corpus.

Abstract 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.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/033c62c07bdbc047adb1fdec6027111be258de14