Compact embeddings of Sobolev, Besov, and Triebel-Lizorkin spaces
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913405740253184 |
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| author | Alvarado, Ryan Górka, Przemysław Słabuszewski, Artur |
| author_facet | Alvarado, Ryan Górka, Przemysław Słabuszewski, Artur |
| contents | We establish necessary and sufficient conditions guaranteeing compactness of embeddings of fractional Sobolev spaces, Besov spaces, and Triebel-Lizorkin spaces, in the general context of quasi-metric-measure spaces. Although stated in the setting of quasi-metric spaces, the main results in this article are new, even in the metric setting. Moreover, by considering the more general category of quasi-metric spaces we are able to obtain these characterizations for optimal ranges of exponents that depend (quantitatively) on the geometric makeup of the underlying space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_18527 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Compact embeddings of Sobolev, Besov, and Triebel-Lizorkin spaces Alvarado, Ryan Górka, Przemysław Słabuszewski, Artur Functional Analysis We establish necessary and sufficient conditions guaranteeing compactness of embeddings of fractional Sobolev spaces, Besov spaces, and Triebel-Lizorkin spaces, in the general context of quasi-metric-measure spaces. Although stated in the setting of quasi-metric spaces, the main results in this article are new, even in the metric setting. Moreover, by considering the more general category of quasi-metric spaces we are able to obtain these characterizations for optimal ranges of exponents that depend (quantitatively) on the geometric makeup of the underlying space. |
| title | Compact embeddings of Sobolev, Besov, and Triebel-Lizorkin spaces |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2406.18527 |