Hardy-Littlewood theory on unimodular groups
type: Item
instance of: scholarly article
title: Hardy-Littlewood theory on unimodular groups
zbMATH Open document ID: 0844.60006
author: N. Th. Varopoulos
published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques
publication date: 1996-08-27T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/77524
review text: The following result on the \(L^\infty\)-estimation of the heat diffusion kernel \(\varphi\) associated with a left invariant subelliptic Laplacian \(\Delta\) on a connected unimodular, nonamenable real Lie group \(G\) is proved: Let \(\lambda\) be the spectral gap of \(\Delta\) and let \(Q\) denote the radical of \(G\). (a) If \(Q\) is of polynomial growth, then \[ |\varphi(t,.)|_{\infty} = O(e^{-\lambda t} t^{-q/2 - D/2}), \] where \(q\) and \(D\) are constants arising from the structure of \(G/Q\) and from bounds to the growth function of \(Q\), respectively. (b) If \(Q\) is of exponential growth, there exists a \(c > 0\) such that \[ |\varphi(t,.)|_{\infty} = O(e^{-\lambda t - c t^{1/3}}). \]
Mathematics Subject Classification ID: 60B15
Mathematics Subject Classification ID: 22E30
Mathematics Subject Classification ID: 60G15
zbMATH DE Number: 812597
zbMATH Keywords: heat kernels
zbMATH Keywords: analysis on Lie groups
zbMATH Keywords: probability measures on groups
reviewed by: Herbert Heyer
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 812597