Nash inequalities for Markov processes in dimension one
type: Item
instance of: scholarly article
title: Nash inequalities for Markov processes in dimension one
zbMATH Open document ID: 1022.60074
author: Young Hua Mao
publication date: 2003-10-27T00:00:00Z
review text: The so-called Nash inequality for a symmetric form \(D\) with a domain \(Q\) in \(L^2(\mu)\) has the form \(\|f\|_2^{2+4/\nu}\leq c D(f,f) \|f\|_1^{4/\nu}\), for \(\nu>2\) and \(f\in\{f\in Q:\mu(f\neq 0)<\infty\}\). The aim of the paper is to give some sufficient and necessary conditions of Nash inequalities for Markov chains and diffusions on the line. Certain results for the general case of \(D\) were obtained by \textit{M. Chen} [Acta Math. Sin., Engl. Ser. 15, 353-370 (1999; Zbl 0938.60067)]. The main tools applied in the present paper are Hardy-type inequalities on the line and the equivalence between the Nash inequality and a certain Sobolev type inequality. Sufficient conditions for general Markov chains are also obtained.
reviewed by: Teresa Regińska
Mathematics Subject Classification ID: 60J25
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60J80
zbMATH DE Number: 1757455
zbMATH Keywords: Nash inequalities
zbMATH Keywords: Hardy type inequality
zbMATH Keywords: birth-death process
zbMATH Keywords: diffusion process
MaRDI profile type: Publication
full work available at URL: s101140100128
OpenAlex ID: W2005675097
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DOI: 10.1007/S101140100128
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 1757455