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

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Title: Hardy and Rellich inequalities, identities, and sharp remainders on homogeneous groups
Authors: Ruzhansky, M
Suragan, D
Item Type: Journal Article
Abstract: We give sharp remainder terms of Lp 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.
Issue Date: 7-Sep-2017
Date of Acceptance: 24-Jul-2017
URI: http://hdl.handle.net/10044/1/50224
DOI: https://dx.doi.org/10.1016/j.aim.2017.07.020
ISSN: 1090-2082
Publisher: Elsevier
Start Page: 799
End Page: 822
Journal / Book Title: Advances in Mathematics
Volume: 317
Copyright Statement: © 2017 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
The Leverhulme Trust
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/K039407/1
RPG-2014-002
EP/R003025/1
Keywords: math.CA
math.AP
math.FA
22E30, 43A80
0101 Pure Mathematics
General Mathematics
Publication Status: Published
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



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