Weak log-Sobolev and <italic>L</italic><sup><italic>p</italic></sup> weak Poincaré inequalities for general symmetric forms

Changsong DENG; Yanhong SONG

doi:10.1007/s11464-012-0199-0

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Front. Math. China ›› 2012, Vol. 7 ›› Issue (6) : 1059-1071. DOI: 10.1007/s11464-012-0199-0

RESEARCH ARTICLE

Weak log-Sobolev and L^p weak Poincaré inequalities for general symmetric forms

Changsong DENG¹^,² ,
Yanhong SONG²

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Abstract

Weak log-Sobolev and L^p 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.

Keywords

Weak log-Sobolev inequality / L^p weak Poincaré inequality / symmetric form / isoperimetric constant

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Changsong DENG, Yanhong SONG. Weak log-Sobolev and L^p weak Poincaré inequalities for general symmetric forms. Front Math Chin, 2012, 7(6): 1059‒1071 https://doi.org/10.1007/s11464-012-0199-0

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