On estimation of the logarithmic Sobolev constant and gradient estimates of heat semigroups

1997 ◽  
Vol 108 (1) ◽  
pp. 87-101 ◽  
Author(s):  
Feng-Yu Wang
Keyword(s):  
Gradient Estimates ◽  
Sobolev Constant ◽  
Heat Semigroups ◽  
Logarithmic Sobolev Constant

Logarithmic Sobolev inequalities for Moebius measures on spheres

2018 ◽  
Vol 30 (1) ◽  
pp. 1-13
Author(s):  
Franck Barthe ◽  
Yutao Ma ◽  
Zhengliang Zhang
Keyword(s):  
Sobolev Inequalities ◽  
Logarithmic Sobolev Inequalities ◽  
One Dimensional ◽  
Information Inequalities ◽  
Sobolev Constant ◽  
Poincaré Constant ◽  
Logarithmic Sobolev Constant

Abstract In this paper, using the method in [1], i.e., reduce Moebius measures {\mu_{x}^{n}} indexed by {|x|<1} on spheres {S^{n-1}} ( {n\geq 3} ) to one-dimensional diffusions on {[0,\pi]} , we obtain that the optimal Poincaré constant is not greater than {\frac{2}{n-2}} and the optimal logarithmic Sobolev constant denoted by {C_{\rm LS}(\mu_{x}^{n})} behaves like {\frac{1}{n}\log(1+\frac{1}{1{-}|x|})} . As a consequence, we claim that logarithmic Sobolev inequalities are strictly stronger than {L^{2}} -transportation-information inequalities.

scholarly journals The logarithmic Sobolev constant of some finite Markov chains

2008 ◽  
Vol 17 (2) ◽  
pp. 239-290 ◽  
Author(s):  
Guan-Yu Chen ◽  
Wai-Wai Liu ◽  
Laurent Saloff-Coste
Keyword(s):  
Markov Chains ◽  
Sobolev Constant ◽  
Finite Markov Chains ◽  
Logarithmic Sobolev Constant
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