Capacitary criteria for Poincaré-type inequalities
type: Item
instance of: scholarly article
title: Capacitary criteria for Poincaré-type inequalities
zbMATH Open document ID: 1076.60064
published in: Potential Analysis
publication date: 2005-06-09T00:00:00Z
review text: Let \(E\) be a locally compact separable metric space and let \((D, {\mathcal D}(D))\) be regular Dirichlet form on a normed linear space \((\mathbf B, \| .\|_{\mathbf B},\mu)\) of real functions on \(E\). Under some natural assumptions on \(\mathbf B\), the author estimates the optimal constant \(A_{\mathbf B}\) in the Poincaré-type inequality (\(\| f^2\|_{\mathbf B}\leq A_{\mathbf B} D(f); f\in {\mathcal D}(D)\cap C_0(E)\)). As in the classical situation, the lower and upper bounds of \(A_{\mathbf B}\) are given, for the transient case and for the recurrent one, in terms of the capacity. This result may be applied for Banach or Orlicz spaces. Moreover, explicit estimations are computed in dimension one.
reviewed by: Mohamed Hmissi
Mathematics Subject Classification ID: 60J55
Mathematics Subject Classification ID: 31C25
Mathematics Subject Classification ID: 60J35
Mathematics Subject Classification ID: 47D07
zbMATH DE Number: 2174536
zbMATH Keywords: Dirichlet form
zbMATH Keywords: isoperimetric constant
zbMATH Keywords: logarithmic Sobolev inequality
zbMATH Keywords: Orlicz space
author: Mu-Fa Chen
MaRDI profile type: Publication
full work available at URL: s11118-005-2609-3
OpenAlex ID: W2030122087
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DOI: 10.1007/S11118-005-2609-3
description: scientific article; zbMATH DE number 2174536