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Sharp defective log-Sobolev inequalities on H-type groups

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arxiv 2410.15566 v1 pith:DPJPVFOU submitted 2024-10-21 math.AP math.FAmath.GR

Gioacchino Antonelli , Mattia Calzi , Maria Gordina This is my paper · ORCID
classification math.APmath.FAmath.GR
keywords defectivegroupsh-typeinequalitylog-sobolevmeasurerespectsharp
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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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  1. Optimal subelliptic super-Poincar\'e and isoperimetric inequalities on stratified Lie groups

    math.PR 2024-11 conditional novelty 7.0 of 10

    Exponential-power measures on stratified Lie groups, Grushin and Heisenberg-Greiner spaces satisfy q-super-Poincaré and isoperimetric inequalities with optimal exponent r=(α+1)p/(α+1+αp).

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