On Supercontractivity for Markov Semigroups  

作　　者：Yong Hua MAO 

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

出　　处：《Acta Mathematica Sinica,English Series》2007年第5期905-914,共10页数学学报（英文版）

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

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.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.

关 键 词：Markov semigroup logarithmic Sobolev inequality supercontractivity compact embedding 

分 类 号：O152.7[理学—数学]