直线上函数的Banach空间的Poincaré型不等式的变分公式

陈木法

数学学报 ›› 2005, Vol. 48 ›› Issue (2) : 209-220.

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数学学报 ›› 2005, Vol. 48 ›› Issue (2) : 209-220. DOI: 10.12386/A2005sxxb0025
论文

直线上函数的Banach空间的Poincaré型不等式的变分公式

    陈木法
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Variational Formulas of Poincare-Type Inequalities in Banach Spaces of Functions on the Line

    Mu Fa CHEN
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摘要

基于研究对数Sobolev,Nash和其它泛函不等式的需要,将Poincare不等式 的变分公式拓广到一大类直线上函数的Banach(Orlicz)空间.给出了这些不等式成立 与否的显式判准和显式估计. 作为典型应用,仔细考察了对数Sobolev常数.

Abstract

Motivated from the study on logarithmic Sobolev, Nash and other functional inequalities, the variational formulas for Poincare inequalities are extended to a large class of Banach (Orlicz) spaces of functions on the line. Explicit criteria for the inequalities to hold and explicit estimates for the optimal constants in the inequalities are presented. As a typical application, the logarithmic Sobolev constant is carefully examined.

关键词

对数Sobolev不等式 / Orlicz空间 / 变分公式 / Poincaré不等式

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陈木法. 直线上函数的Banach空间的Poincaré型不等式的变分公式. 数学学报, 2005, 48(2): 209-220 https://doi.org/10.12386/A2005sxxb0025
Mu Fa CHEN. Variational Formulas of Poincare-Type Inequalities in Banach Spaces of Functions on the Line. Acta Mathematica Sinica, Chinese Series, 2005, 48(2): 209-220 https://doi.org/10.12386/A2005sxxb0025
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