Bourgain-Brezis-Mironescu formula for $W^{s,p}_q$-spaces in arbitrary domains
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866911750883901440 |
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| author | Mohanta, Kaushik |
| author_facet | Mohanta, Kaushik |
| contents | Under certain restrictions on $s,p,q$, the Triebel-Lizorkin spaces can be viewed as generalised fractional Sobolev spaces $W^{s,p}_q$. In this article, we show that the Bourgain-Brezis-Mironescu formula holds for $W^{s,p}_q$-seminorms in arbitrary domain. This addresses an open question raised by Brazke-Schikorra-Yung in [Bourgain-Brezis-Mironescu convergence via Triebel-Lizorkin spaces; Calc. Var. Partial Differential Equations; 2023]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_12830 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Bourgain-Brezis-Mironescu formula for $W^{s,p}_q$-spaces in arbitrary domains Mohanta, Kaushik Functional Analysis Analysis of PDEs 46E35, 42B35 Under certain restrictions on $s,p,q$, the Triebel-Lizorkin spaces can be viewed as generalised fractional Sobolev spaces $W^{s,p}_q$. In this article, we show that the Bourgain-Brezis-Mironescu formula holds for $W^{s,p}_q$-seminorms in arbitrary domain. This addresses an open question raised by Brazke-Schikorra-Yung in [Bourgain-Brezis-Mironescu convergence via Triebel-Lizorkin spaces; Calc. Var. Partial Differential Equations; 2023]. |
| title | Bourgain-Brezis-Mironescu formula for $W^{s,p}_q$-spaces in arbitrary domains |
| topic | Functional Analysis Analysis of PDEs 46E35, 42B35 |
| url | https://arxiv.org/abs/2308.12830 |