On the Bourgain, Brezis, and Mironescu theorem concerning limiting embeddings of fractional Sobolev spaces

V. Maz'ya; T. Shaposhnikova

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On the Bourgain, Brezis, and Mironescu theorem concerning limiting embeddings of fractional Sobolev spaces

Maz'ya V
Shaposhnikova T

Journal of Functional Analysis (2002) 195(2) 230-238

DOI: 10.1006/jfan.2002.3955

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Abstract

The article is concerned with the Bourgain, Brezis and Mironescu theorem on the asymptotic behaviour of the norm of the Sobolev-type embedding operator: Ws,p → Lpn/(n-sp) as s ↑ 1 and s ↑ n/p. Their result is extended to all values of s ∈ (0, 1) and is supplied with an elementary proof. The relation is proved. © 2002 Elsevier Science (USA).

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Maz’ya, V., & Shaposhnikova, T. (2002). On the Bourgain, Brezis, and Mironescu theorem concerning limiting embeddings of fractional Sobolev spaces. Journal of Functional Analysis, 195(2), 230–238. https://doi.org/10.1006/jfan.2002.3955

On the Bourgain, Brezis, and Mironescu theorem concerning limiting embeddings of fractional Sobolev spaces

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