Regularity of Characteristic Functions in Besov-Type and Triebel--Lizorkin-Type Spaces
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909408061030400 |
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| author | Yuan, Wen Sickel, Winfried Yang, Dachun |
| author_facet | Yuan, Wen Sickel, Winfried Yang, Dachun |
| contents | In this article, the authors determine the optimal regularity of characteristic functions in Besov-type and Triebel--Lizorkin-type spaces under restrictions on the measure of the $δ$-neighborhoods of the boundary. In particular, the necessary and sufficient conditions for the membership in these spaces of characteristic functions of the snowflake domain and also some spiral type domains are obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_19153 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Regularity of Characteristic Functions in Besov-Type and Triebel--Lizorkin-Type Spaces Yuan, Wen Sickel, Winfried Yang, Dachun Functional Analysis Analysis of PDEs Classical Analysis and ODEs Primary 46E35, Secondary 42C15 In this article, the authors determine the optimal regularity of characteristic functions in Besov-type and Triebel--Lizorkin-type spaces under restrictions on the measure of the $δ$-neighborhoods of the boundary. In particular, the necessary and sufficient conditions for the membership in these spaces of characteristic functions of the snowflake domain and also some spiral type domains are obtained. |
| title | Regularity of Characteristic Functions in Besov-Type and Triebel--Lizorkin-Type Spaces |
| topic | Functional Analysis Analysis of PDEs Classical Analysis and ODEs Primary 46E35, Secondary 42C15 |
| url | https://arxiv.org/abs/2411.19153 |