Sharp fractional Sobolev and related inequalities on H-type groups
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909232233709568 |
|---|---|
| author | Wang, Yaojun Yang, Qiaohua |
| author_facet | Wang, Yaojun Yang, Qiaohua |
| contents | We determine the sharp constants for the fractional Sobolev inequalities associated with the conformally invariant fractional powers $\mathcal{L}_{s}(0<s<1)$ of the sublaplacian on H-type groups. From these inequalities we derive a sharp log-Sobolev inequality by considering a limiting case and a sharp Sobolev trace inequality. The later extends to this context the result of Frank, González, Monticelli and Tan (Adv. Math, 2015). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_16278 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sharp fractional Sobolev and related inequalities on H-type groups Wang, Yaojun Yang, Qiaohua Analysis of PDEs We determine the sharp constants for the fractional Sobolev inequalities associated with the conformally invariant fractional powers $\mathcal{L}_{s}(0<s<1)$ of the sublaplacian on H-type groups. From these inequalities we derive a sharp log-Sobolev inequality by considering a limiting case and a sharp Sobolev trace inequality. The later extends to this context the result of Frank, González, Monticelli and Tan (Adv. Math, 2015). |
| title | Sharp fractional Sobolev and related inequalities on H-type groups |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2406.16278 |