Harnack inequalities for log-Sobolev functions and estimates of log-Sobolev constants

• 成果类型: Article
• 署名作者: Wang, FY
• 署名单位: Beijing Normal University; University of Bielefeld
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1022677381
• 发表日期: 1999
• 页码: 653-663
• 关键词: eigenvalue; MANIFOLDS

摘要

By using the maximum principle and analysis of heat semigroups, Harnack inequalities are studied for log-Sobolev functions. From this, some lower bound estimates of the log-Sobolev constant are presented by using the spectral gap inequality and the coupling method. The resulting inequalities either recover or improve the corresponding ones proved by Chung and Yau. Especially, Harnack inequalities and estimates of log-Sobolev constants can be dimension-free.