Modified Logarithmic Sobolev Inequalities and Transportation Cost Inequalities in Rn

被引：2

作者：

Shao, Jinghai ^{[1
]}

机构：

[1] Beijing Normal Univ, Sch Math, Beijing 100875, Peoples R China

来源：

POTENTIAL ANALYSIS | 2009年 / 31卷 / 02期

关键词：

Modified logarithmic Sobolev inequalities; Prekopa-Leindler inequalities; Hamilton-Jacobi semigroups; Transportation cost inequalities; BRUNN-MINKOWSKI; LOG-SOBOLEV; POINCARE; BRASCAMP;

D O I：

10.1007/s11118-009-9131-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, the modified logarithmic Sobolev inequalities and transportation cost inequalities for measures with density e(-V) in R-n are established. It is proved by using Prekopa-Leindler inequalities following the idea of Bobkov-Ledoux, but a different type of condition is used which recovers Bakry-Emery criterion. As an application, we establish the modified logarithmic Sobolev and transportation cost inequalities for probability measures e(-vertical bar x vertical bar p) dx/Z(p) with p > 1 in R-n, and give out explicit estimates for their constants.

引用

页码：183 / 202

页数：20

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