Frontiers of Mathematics in China >

2012 , Vol. 7 >Issue 6: 1059 - 1071

DOI: https://doi.org/10.1007/s11464-012-0199-0

RESEARCH ARTICLE

Weak log-Sobolev and Lp weak Poincaré inequalities for general symmetric forms

  • Changsong DENG 1,2 ,
  • Yanhong SONG , 2
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  • 1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • 2. School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems (Beijing Normal University), Ministry of Education, Beijing 100875, China

Received date: 22 Apr 2011

Accepted date: 20 Feb 2012

Published date: 01 Dec 2012

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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Abstract

Weak log-Sobolev and Lp weak Poincaré inequalities for general symmetric forms are investigated by using newly defined Cheeger’s isoperimetric constants. Some concrete examples of ergodic birth-death processes are also presented to illustrate the results.

Key words： Weak log-Sobolev inequality; Lp weak Poincaré inequality; symmetric form; isoperimetric constant

Cite this article

Changsong DENG , Yanhong SONG . Weak log-Sobolev and Lp weak Poincaré inequalities for general symmetric forms[J]. Frontiers of Mathematics in China, 2012 , 7(6) : 1059 -1071 . DOI: 10.1007/s11464-012-0199-0

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