Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2409.18720 |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866917788706144256 |
|---|---|
| author | Wang, Zhiyong Li, Pengtao Liu, Yu |
| author_facet | Wang, Zhiyong Li, Pengtao Liu, Yu |
| contents | In this paper, we focus on the functional and geometrical aspects of the fractional Sobolev capacity, the Besov capacity and the Riesz capacity on stratified lie groups, respectively. Firstly, we provide a new Carleson characterization of the extension of fractional Sobolev spaces to $L^{q}(\X\times\mathbb{R}_{+},μ)$ with $q\in\mathbb{R}_{+}$ using the fractional heat semigroup and the Caffarelli-Silvestre type extension on stratified Lie groups $\X$. Secondly, a characterization of $ν$ on $\X$ which ensures the continuity of the fractional Sobolev space belonging to $L^{q}(\X,ν)$ is also obtained via taking $t\rightarrow 0$. Finally, with the help of inequalities related to the Besov capacity and its properties, we also obtain a characterization of $ν$ on $\X$ which ensures the continuity of the Besov type space belonging to $L^{q}(\X,ν)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_18720 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Several functional capacities and Carleson type embeddings of fractional Sobolev sapces on stratified Lie groups Wang, Zhiyong Li, Pengtao Liu, Yu Analysis of PDEs 31B15, 43A80, 26A33 In this paper, we focus on the functional and geometrical aspects of the fractional Sobolev capacity, the Besov capacity and the Riesz capacity on stratified lie groups, respectively. Firstly, we provide a new Carleson characterization of the extension of fractional Sobolev spaces to $L^{q}(\X\times\mathbb{R}_{+},μ)$ with $q\in\mathbb{R}_{+}$ using the fractional heat semigroup and the Caffarelli-Silvestre type extension on stratified Lie groups $\X$. Secondly, a characterization of $ν$ on $\X$ which ensures the continuity of the fractional Sobolev space belonging to $L^{q}(\X,ν)$ is also obtained via taking $t\rightarrow 0$. Finally, with the help of inequalities related to the Besov capacity and its properties, we also obtain a characterization of $ν$ on $\X$ which ensures the continuity of the Besov type space belonging to $L^{q}(\X,ν)$. |
| title | Several functional capacities and Carleson type embeddings of fractional Sobolev sapces on stratified Lie groups |
| topic | Analysis of PDEs 31B15, 43A80, 26A33 |
| url | https://arxiv.org/abs/2409.18720 |