Note on the $q$-Logarithmic Sobolev and $p$-Talagrand Inequalities on Carnot Groups
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2021
- DOI:
- 10.48550/arXiv.2105.04928
- arXiv:
- arXiv:2105.04928
- Bibcode:
- 2021arXiv210504928D
- Keywords:
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- Mathematics - Functional Analysis;
- 22E30;
- 26D10;
- 39B62
- E-Print:
- 16 pages