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arXiv · 2105.04928

Note on the $q$-Logarithmic Sobolev and $p$-Talagrand Inequalities on Carnot Groups

Esther Bou Dagher
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Abstract

In the setting of Carnot groups, we prove the $q-$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 $p-$Talagrand inequality and hypercontractivity.

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Esther Bou Dagher. 2021-05-11. Note on the $q$-Logarithmic Sobolev and $p$-Talagrand Inequalities on Carnot Groups. https://doi.org/10.1142/s0219199722500705

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