Classifying Triebel-Lizorkin capacities in metric spaces
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916166154321920 |
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| author | Lehrbäck, Juha Mohanta, Kaushik Vähäkangas, Antti V. |
| author_facet | Lehrbäck, Juha Mohanta, Kaushik Vähäkangas, Antti V. |
| contents | We study non-local or fractional capacities in metric measure spaces. Our main goal is to clarify the relations between relative Hajlasz-Triebel-Lizorkin capacities, potentional Triebel-Lizorkin capacities, and metric space variants of Riesz capacities. As an application of our results, we obtain a characterization of a Hajlasz-Triebel-Lizorkin capacity density condition, which is based on an earlier characterization of a Riesz capacity density condition in terms of Hausdorff contents. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_12513 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classifying Triebel-Lizorkin capacities in metric spaces Lehrbäck, Juha Mohanta, Kaushik Vähäkangas, Antti V. Classical Analysis and ODEs Analysis of PDEs 31C15 (28A12, 31E05) We study non-local or fractional capacities in metric measure spaces. Our main goal is to clarify the relations between relative Hajlasz-Triebel-Lizorkin capacities, potentional Triebel-Lizorkin capacities, and metric space variants of Riesz capacities. As an application of our results, we obtain a characterization of a Hajlasz-Triebel-Lizorkin capacity density condition, which is based on an earlier characterization of a Riesz capacity density condition in terms of Hausdorff contents. |
| title | Classifying Triebel-Lizorkin capacities in metric spaces |
| topic | Classical Analysis and ODEs Analysis of PDEs 31C15 (28A12, 31E05) |
| url | https://arxiv.org/abs/2403.12513 |