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arXiv · 1311.3989

Strong Logarithmic Sobolev Inequalities for Log-Subharmonic Functions

Piotr Graczyk·Todd Kemp·Jean-Jacques Loeb
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Abstract

We prove an intrinsic equivalence between strong hypercontractivity and a strong logarithmic Sobolev inequality for the cone of logarithmically subharmonic 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 log-subharmonic functions, and use it to prove the equivalence of strong hypercontractivity and the strong log Sobolev inequality for such log-subharmonic functions.

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Piotr Graczyk, Todd Kemp, Jean-Jacques Loeb. 2013-11-15. Strong Logarithmic Sobolev Inequalities for Log-Subharmonic Functions. https://doi.org/10.4153/cjm-2015-015-8

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