The Annals of Probability

Harnack Inequalities for Log-Sobolev Functions and Estimates of Log-Sobolev Constants

Feng-Yu Wang

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Abstract

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.

Article information

Source
Ann. Probab. Volume 27, Number 2 (1999), 653-663.

Dates
First available: 29 May 2002

Permanent link to this document
http://projecteuclid.org/euclid.aop/1022677381

Mathematical Reviews number (MathSciNet)
MR1698947

Digital Object Identifier
doi:10.1214/aop/1022677381

Zentralblatt MATH identifier
0948.58023

Subjects
Primary: 58G32 60J60: Diffusion processes [See also 58J65]

Keywords
Harnack inequality log-Sobolev function log-Sobolev constant coupling method

Citation

Wang, Feng-Yu. Harnack Inequalities for Log-Sobolev Functions and Estimates of Log-Sobolev Constants. The Annals of Probability 27 (1999), no. 2, 653--663. doi:10.1214/aop/1022677381. http://projecteuclid.org/euclid.aop/1022677381.


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