On Supercontractivity for Markov Semigroups

被引：0
作者：
Yong Hua Mao
机构：
[1] Beijing Normal University,School of Mathematical Science
来源：
Acta Mathematica Sinica, English Series | 2007年 / 23卷
关键词：
Markov semigroup; logarithmic Sobolev inequality; supercontractivity; compact embedding; 46E35; 60J60; 60J75;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we study the supercontractivity for Markov 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.
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页码：905 / 914
页数：9
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