Sharp defective log-Sobolev inequalities on H-type groups
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929551676801024 |
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| author | Antonelli, Gioacchino Calzi, Mattia Gordina, Maria |
| author_facet | Antonelli, Gioacchino Calzi, Mattia Gordina, Maria |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_15566 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sharp defective log-Sobolev inequalities on H-type groups Antonelli, Gioacchino Calzi, Mattia Gordina, Maria Analysis of PDEs Functional Analysis Group Theory 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. |
| title | Sharp defective log-Sobolev inequalities on H-type groups |
| topic | Analysis of PDEs Functional Analysis Group Theory |
| url | https://arxiv.org/abs/2410.15566 |