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December 2007 Interpolation between logarithmic Sobolev and Poincare inequalities
Anton Arnold, Jean-Philippe Bartier, Jean Dolbeault
Commun. Math. Sci. 5(4): 971-979 (December 2007).


This paper is concerned with intermediate inequalities which interpolate between the logarithmic Sobolev (LSI) and the Poincaré inequalities. Assuming that a given probability measure gives rise to a LSI, we derive generalized Poincaré inequalities, improving upon the known constants from the literature. We also analyze the special case when these inequalities are restricted to functions with zero components for the first eigenspaces of the corresponding evolution operator.


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Anton Arnold. Jean-Philippe Bartier. Jean Dolbeault. "Interpolation between logarithmic Sobolev and Poincare inequalities." Commun. Math. Sci. 5 (4) 971 - 979, December 2007.


Published: December 2007
First available in Project Euclid: 3 January 2008

zbMATH: 1146.60063
MathSciNet: MR2375056

Primary: 35K10 , ‎39B62 , 46E35 , 60F10 , 60J60

Keywords: functional inequalities , hypercontractivity , Logarithmic Sobolev inequality , Poincaré inequality , spectral gap

Rights: Copyright © 2007 International Press of Boston

Vol.5 • No. 4 • December 2007
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