Bourgain-Brezis-Mironescu formula for \(W^{s, p}_q\)-spaces in arbitrary domains. (English) Zbl 1542.46029
Summary: 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
[D. Brazke et al., Calc. Var. Partial Differ. Equ. 62, No. 2, Paper No. 41, 33 p. (2023; Zbl 1508.46024)].
MSC:
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
| 42B35 | Function spaces arising in harmonic analysis |
Keywords:
Bourgain-Brezis-Mironescu formulaCitations:
Zbl 1508.46024References:
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