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Strong Logarithmic Sobolev Inequalities for Log-Subharmonic Functions

Abstract : We prove an intrinsic equivalence between strong hypercontractivity and a strong logarithmic Sobolev inequality for the cone of logarithmically subharmonic (LSH) functions. We introduce a new large class of measures, Euclidean regular and exponential type, in addition to all compactly-supported measures, for which this equivalence holds. We prove a Sobolev density theorem through LSH functions, and use it to prove the equivalence of strong hypercontractivity and strong logarithmic Sobolev inequality for such log-subharmonic functions.
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https://hal.archives-ouvertes.fr/hal-00906171
Contributor : Piotr Graczyk <>
Submitted on : Wednesday, November 27, 2013 - 10:03:04 PM
Last modification on : Monday, March 9, 2020 - 6:15:58 PM
Document(s) archivé(s) le : Friday, February 28, 2014 - 4:36:31 AM

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  • HAL Id : hal-00906171, version 1

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Piotr Graczyk, Todd Kemp, Jean-Jacques Loeb. Strong Logarithmic Sobolev Inequalities for Log-Subharmonic Functions. 2013. ⟨hal-00906171⟩

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