Bourgain-Brezis-Mironescu convergence via Triebel-Lizorkin spaces
We study a convergence result of Bourgain--Brezis--Mironescu (BBM) using Triebel-Lizorkin spaces. It is well known that as spaces $W^{s,p} = F^{s}_{p,p}$, and $H^{1,p} = F^{1}_{p,2}$. When $s\to 1$, the $F^{s}_{p,p}$ norm becomes the $F^{1}_{p,p}$ norm but BBM showed that the $W^{s,p}$ norm becomes...
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| Main Authors: | , , |
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| Format: | Article (Journal) Chapter/Article |
| Language: | English |
| Published: |
9 Sep 2021
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| In: |
Arxiv
Year: 2021, Pages: 1-24 |
| DOI: | 10.48550/arXiv.2109.04159 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.48550/arXiv.2109.04159 Verlag, lizenzpflichtig, Volltext: http://arxiv.org/abs/2109.04159 
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| Author Notes: | Denis Brazke, Armin Schikorra, and Po-Lam Yung |
| Summary: | We study a convergence result of Bourgain--Brezis--Mironescu (BBM) using Triebel-Lizorkin spaces. It is well known that as spaces $W^{s,p} = F^{s}_{p,p}$, and $H^{1,p} = F^{1}_{p,2}$. When $s\to 1$, the $F^{s}_{p,p}$ norm becomes the $F^{1}_{p,p}$ norm but BBM showed that the $W^{s,p}$ norm becomes the $H^{1,p} = F^{1}_{p,2}$ norm. Naively, for |
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| Item Description: | Gesehen am 28.09.2022 |
| Physical Description: | Online Resource |
| DOI: | 10.48550/arXiv.2109.04159 |