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arXiv · 2410.15566

Sharp defective log-Sobolev inequalities on H-type groups

Gioacchino Antonelli·Mattia Calzi·Maria Gordina
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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.

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Gioacchino Antonelli, Mattia Calzi, Maria Gordina. 2024-10-21. Sharp defective log-Sobolev inequalities on H-type groups. https://arxiv.org/abs/2410.15566

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