Bourgain-Brezis-Mironescu formula for Ws,pq-spaces in arbitrary domains
Abstract
Under certain restrictions on s,p,q, the Triebel-Lizorkin spaces can be viewed as generalised fractional Sobolev spaces Ws,pq. In this article, we show that the Bourgain-Brezis-Mironescu formula holds for Ws,pq-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].
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