Strong Logarithmic Sobolev Inequalities for Log-Subharmonic Functions
Functional Analysis
2019-08-15 v1
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.
Cite
@article{arxiv.1311.3989,
title = {Strong Logarithmic Sobolev Inequalities for Log-Subharmonic Functions},
author = {Piotr Graczyk and Todd Kemp and Jean-Jacques Loeb},
journal= {arXiv preprint arXiv:1311.3989},
year = {2019}
}