Strong hypercontractivity and logarithmic Sobolev inequalities on stratified complex Lie groups
Analysis of PDEs
2018-11-30 v5 Functional Analysis
Probability
Abstract
We show that for a hypoelliptic Dirichlet form operator A on a stratified complex Lie group, if the logarithmic Sobolev inequality holds, then a holomorphic projection of A is strongly hypercontractive in the sense of Janson. This extends previous results of Gross to a setting in which the operator A is not holomorphic.
Keywords
Cite
@article{arxiv.1510.05151,
title = {Strong hypercontractivity and logarithmic Sobolev inequalities on stratified complex Lie groups},
author = {Nathaniel Eldredge and Leonard Gross and Laurent Saloff-Coste},
journal= {arXiv preprint arXiv:1510.05151},
year = {2018}
}
Comments
46 pages. Minor corrections. To appear in Transactions of the American Mathematical Society