Harnack and HWI Inequalities on Infinite-Dimensional Spaces  

作　　者：Jing Hai SHAO 

机构地区：[1]School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2011年第6期1195-1204,共10页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China （Grant No. 10721091） and the 973-Project （Grant No. 2006CB805901）

摘　　要：In this paper, the dimensional-free Harnack inequalities are established on infinite-dimen- sional spaces. More precisely, we establish Harnack inequalities for heat semigroup on based loop group and for Ornstein-Uhlenbeck semigroup on the abstract Wiener space. As an application, we establish the HWI inequality on the abstract Wiener space, which contains three important quantities in one inequality, the relative entropy ＂H＂, Wasserstein distance ＂W＂, and Fisher information ＂T＂.In this paper, the dimensional-free Harnack inequalities are established on infinite-dimen- sional spaces. More precisely, we establish Harnack inequalities for heat semigroup on based loop group and for Ornstein-Uhlenbeck semigroup on the abstract Wiener space. As an application, we establish the HWI inequality on the abstract Wiener space, which contains three important quantities in one inequality, the relative entropy ＂H＂, Wasserstein distance ＂W＂, and Fisher information ＂T＂.

关 键 词：Harnack inequality loop groups HWI inequality abstract Wiener space Ornstein- Uhlenbeck semigroup 

分 类 号：O177.2[理学—数学] O175.26[理学—基础数学]