Sharp defective log-Sobolev inequalities on H-type groups
Analysis of PDEs
2024-10-22 v1 Functional Analysis
Group Theory
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.
Keywords
Cite
@article{arxiv.2410.15566,
title = {Sharp defective log-Sobolev inequalities on H-type groups},
author = {Gioacchino Antonelli and Mattia Calzi and Maria Gordina},
journal= {arXiv preprint arXiv:2410.15566},
year = {2024}
}
Comments
20 pages. Comments are welcome!