Asymptotic Behaviour of fractional seminorms
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911254619095040 |
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| author | Dughayshim, Ahmed |
| author_facet | Dughayshim, Ahmed |
| contents | We obtain asymptotically sharp identification of fractional Sobolev spaces $ W^{s}_{p,q}$, extension spaces $E^{s}_{p,q}$, and Triebel-Lizorkin spaces $\dot{F}^s_{p,q}$. In particular we obtain for $W^{s}_{p,q}$ and $E^{s}_{p,q}$ a stability theory a la Bourgain-Brezis-Mironescu as $s \to 1$, answering a question raised by Brazke--Schikorra--Yung. Part of the results are new even for $p=q$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_16894 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotic Behaviour of fractional seminorms Dughayshim, Ahmed Analysis of PDEs Functional Analysis 42B35 We obtain asymptotically sharp identification of fractional Sobolev spaces $ W^{s}_{p,q}$, extension spaces $E^{s}_{p,q}$, and Triebel-Lizorkin spaces $\dot{F}^s_{p,q}$. In particular we obtain for $W^{s}_{p,q}$ and $E^{s}_{p,q}$ a stability theory a la Bourgain-Brezis-Mironescu as $s \to 1$, answering a question raised by Brazke--Schikorra--Yung. Part of the results are new even for $p=q$. |
| title | Asymptotic Behaviour of fractional seminorms |
| topic | Analysis of PDEs Functional Analysis 42B35 |
| url | https://arxiv.org/abs/2408.16894 |