Variational formulas of Poincaré-type inequalities in Banach spaces of functions on the line.
type: Item
instance of: scholarly article
title: Variational formulas of Poincaré-type inequalities in Banach spaces of functions on the line.
zbMATH Open document ID: 1063.26008
publication date: 2003-04-13T00:00:00Z
review text: The author extends the variational formulas for (one-dimensional) Poin\-caré-type inequalities to the class of Banach function spaces. A particular attention is devoted to Orlicz spaces. He establishes explicit criteria for the inequalities to hold and explicit estimates of the optimal constants in the inequalities in question. As an application, the logarithmic Sobolev inequality is examined.
Mathematics Subject Classification ID: 26D10
Mathematics Subject Classification ID: 49R50
Mathematics Subject Classification ID: 34L15
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 1885841
zbMATH Keywords: variational formula
zbMATH Keywords: Poincaré inequality
zbMATH Keywords: Banach function space
zbMATH Keywords: Orlicz space
zbMATH Keywords: logarithmic Sobolev inequality
author: Mu-Fa Chen
reviewed by: Bohumír Opic
MaRDI profile type: Publication
full work available at URL: s10114-002-0176-8
OpenAlex ID: W2036597050
DOI: 10.1007/S10114-002-0176-8
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 1885841