Analyse sur les groupes de Lie à croissance polynômiale. (Analysis on Lie groups of polynomial growth)
type: Item
instance of: scholarly article
title: Analyse sur les groupes de Lie à croissance polynômiale. (Analysis on Lie groups of polynomial growth)
zbMATH Open document ID: 0715.43009
DOI: 10.1007/BF02387385
published in: Arkiv för Matematik
publication date: 1990-01-01T00:00:00Z
review text: Let G be a connected real Lie group with the property that there is a positive integer D such that for any symmetric compact neighborhood \(\Omega\) of the unit element in G, we have \(| \Omega^ n| \cong n^ D\) for \(n=1,2,...\), where \(| \Omega |\) is the volume of \(\Omega\) in G. For instance nilpotent Lie groups have the property above. For analysis on G the following is investigated: the Lipschitz space, the Sobolev theorem, the inequality of Trudinger, the Hardy space \(H^ 1\), the Riesz transform, and the Harnack theorem. Sharp estimates for the heat kernel on G are used in this analysis.
reviewed by: Koichi Saka
Mathematics Subject Classification ID: 43A80
Mathematics Subject Classification ID: 22E30
Mathematics Subject Classification ID: 22E25
zbMATH DE Number: 4177853
zbMATH Keywords: connected real Lie group
zbMATH Keywords: volume
zbMATH Keywords: nilpotent Lie groups
zbMATH Keywords: Lipschitz space
zbMATH Keywords: Sobolev theorem
zbMATH Keywords: Hardy space
zbMATH Keywords: Riesz transform
zbMATH Keywords: Harnack theorem
zbMATH Keywords: heat kernel
author: Laurent Saloff-Coste
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4177853