直线上函数的Banach空间的Poincaré型不等式的变分公式  

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

作　　者：陈木法[1] 

机构地区：[1]北京师范大学数学系,北京100875

出　　处：《数学学报（中文版）》2005年第2期209-220,共12页Acta Mathematica Sinica：Chinese Series

基　　金：973项目国家自然科学基金(10121101)教育部博士点专项基金资助项目

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.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：变分公式 POINCARÉ不等式 对数SOBOLEV不等式 ORLICZ空间 

分 类 号：O221.6[理学—运筹学与控制论]