On limiting embeddings of Besov spaces
V. I. Kolyada, A. K. Lerner (2005)
Studia Mathematica
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We investigate the classical embedding . The sharp asymptotic behaviour as s → 1 of the operator norm of this embedding is found. In particular, our result yields a refinement of the Bourgain, Brezis and Mironescu theorem concerning an analogous problem for the Sobolev-type embedding. We also give a different, elementary proof of the latter theorem.