Bourgain-Brezis-Mironescu formula for $W^{s,p}_q$-spaces in arbitrary domains
Abstract
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].
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2023
- DOI:
- 10.48550/arXiv.2308.12830
- arXiv:
- arXiv:2308.12830
- Bibcode:
- 2023arXiv230812830M
- Keywords:
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- Mathematics - Functional Analysis;
- Mathematics - Analysis of PDEs;
- 46E35;
- 42B35
- E-Print:
- Calc. Var. 63, 31 (2024)