A variant of the Hardy inequality
type: Item
instance of: scholarly article
title: A variant of the Hardy inequality
zbMATH Open document ID: 1118.22004
author: Noël Lohoué
published in: Manuscripta Mathematica
publication date: 2007-06-07T00:00:00Z
review text: The inequality of Hardy is proven for Lie groups and some previous results on the same subject are generalized or presented in a simpler form. The author considers a unimodular Lie group \(G\) endowed with a Haar measure and denotes by \(L_{pq}(G) \) the associated Lorentz space. For a given system of vector fields \(X_{1},X_{2},\dots,X_{m}\) the associated sub-Laplacian \(\Delta =-(X_{1}^{2}+\cdots+X_{m}^{2})\) is constructed and the corresponding semigroup \(P_{t}\) is introduced. A proof of the Hardy inequality is given and some comments are added. It is emphasized that the result obtained in this paper can be used to prove a theorem on the existence of solutions to the \(p\)-sub-Laplacian in the case of nilpotent groups with dilatations.
Mathematics Subject Classification ID: 22E30
Mathematics Subject Classification ID: 43A90
Mathematics Subject Classification ID: 60B99
Mathematics Subject Classification ID: 60J60
zbMATH DE Number: 5162388
zbMATH Keywords: unimodular Lie group
zbMATH Keywords: Haar measure
zbMATH Keywords: Lorentz space
zbMATH Keywords: Hardy inequality
zbMATH Keywords: sub-Laplacian
reviewed by: Gheorghe Zet
MaRDI profile type: Publication
full work available at URL: s00229-007-0084-4
OpenAlex ID: W2018715750
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DOI: 10.1007/S00229-007-0084-4
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description: scientific article; zbMATH DE number 5162388