paper

Sharp defective log-Sobolev inequalities on H-type groups

arXiv:2410.15566

Abstract

In this paper we prove a sharp defective log-Sobolev inequality on H-type groups. Then we use such an inequality to show exponential integrability of Lipschitz functions with respect to the heat kernel measure. A defective log-Sobolev-type inequality for the Gaussian-like measure with respect to the sub-Riemannian distance is also proved on arbitrary H-type groups.

20 pages. Comments are welcome!

Sharp defective log-Sobolev inequalities on H-type groups · wovepaper