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Note on the $q$ -logarithmic Sobolev and $p$ -Talagrand inequalities on Carnot groups

Esther Bou Dagher

Department of Mathematics, Imperial College London, 180 Queen’s Gate, London SW7 2AZ, UK

https://doi.org/10.1142/S0219199722500705Cited by:3 (Source: Crossref)

Abstract

In the setting of Carnot groups, we prove the $q$ -logarithmic Sobolev inequality for probability measures as a function of the Carnot–Carathéodory distance. As an application, we use the Hamilton–Jacobi equation in the setting of Carnot groups to prove the $p$ -Talagrand inequality and hypercontractivity.

Keywords:

AMSC: 22E30, 26D10, 39B62

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