On Supercontractivity for Markov Semigroups

作     者：Yong Hua MAO 

作者机构：School of Mathematical Science Beijing Normal University Beijing 100875 P. R. China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2007年第23卷第5期

页      面：905-914页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Research supported in part by RFDP(No 20010027007) 973 Project NSFC(No 10121101,No 10025105 and No 10301007) 

主　　题：Markov semigroup logarithmic Sobolev inequality supercontractivity compact embedding 

摘      要：In this paper, we study the supercontractivity for Maxkov semigroups and obtain some sufficient and necessary conditions; especially explicit formulae are obtained for birth-death process and diffusion on the line. Sufficient conditions and necessary conditions in terms of isoperimetric inequalities are also presented. Moreover, we prove that the supercontractivity is equivalent to the compact embedding of Sobolev space into an Orlicz space.