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 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.

Cited by in corpus (2)

• Strong hypercontractivity and strong logarithmic Sobolev inequalities for log-subharmonic functions on stratified Lie groups
• Strong hypercontractivity and logarithmic Sobolev inequalities on stratified complex Lie groups