Closability of Dirichlet forms and Poincaré-type inequalities
type: Item
instance of: scholarly article
title: Closability of Dirichlet forms and Poincaré-type inequalities
zbMATH Open document ID: 0844.31006
DOI: 10.1007/BF01053455
author: Gabriel Mokobodzki
published in: Potential Analysis
publication date: 1996-09-02T00:00:00Z
review text: Let \(X\) be a locally compact space with countable basis, \(m\) a bounded measure on \(X\), and \(H \subset C_0 (X)\) a dense vector lattice stable for contractions. Let \(a\) be a quadratic form on \(H\) such that the contraction operates on \(a\). A positive measure \(\nu\) is said to satisfy the Poincaré inequality on an open subset \(\omega \subset X\) if \(\int u^2 d \nu \leq Ca (u,u)\) for all \(u \in H\) with compact support contained in \(\omega\). In this paper the author studies the relation between the closability of the form \(a\) and the existence of sufficiently many measures \(\nu\) satisfying the Poincaré inequality on open subsets of \(X\).
reviewed by: Zoran Vondraček
Mathematics Subject Classification ID: 31C25
Mathematics Subject Classification ID: 60J40
zbMATH DE Number: 819162
zbMATH Keywords: Dirichlet forms
zbMATH Keywords: Poincaré inequality
zbMATH Keywords: closability
MaRDI profile type: Publication
cites work: Q3855442
cites work: On the closable parts of pre-Dirichlet forms and the fine supports of underlying measures
cites work: Symmetric Markov processes
full work available at URL: https://doi.org/10.1007/bf01053455
OpenAlex ID: W2076771540
description: scientific article; zbMATH DE number 819162