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.
出处
《数学学报(中文版)》
SCIE
CSCD
北大核心
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