Article contents
Strong Logarithmic Sobolev Inequalities for Log-Subharmonic Functions
Published online by Cambridge University Press: 20 November 2018
Abstract
We prove an intrinsic equivalence between strong hypercontractivity and a strong logarithmic Sobolev inequality for the cone of logarithmically subharmonic ($\text{LSH}$) 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 $\text{LSH}$ functions and use it to prove the equivalence of strong hypercontractivity and the strong logarithmic Sobolev inequality for such log-subharmonic functions.
- Type
- Research Article
- Information
- Copyright
- Copyright © Canadian Mathematical Society 2015
References
- 2
- Cited by