Note on the $q$-Logarithmic Sobolev and $p$-Talagrand Inequalities on Carnot Groups
Functional Analysis
2022-11-01 v1
Abstract
In the setting of Carnot groups, we prove the Logarithmic Sobolev inequality for probability measures as a function of the Carnot-Carath\'eodory distance. As an application, we use the Hamilton-Jacobi equation in the setting of Carnot groups to prove the Talagrand inequality and hypercontractivity.
Keywords
Cite
@article{arxiv.2105.04928,
title = {Note on the $q$-Logarithmic Sobolev and $p$-Talagrand Inequalities on Carnot Groups},
author = {Esther Bou Dagher},
journal= {arXiv preprint arXiv:2105.04928},
year = {2022}
}
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16 pages