On limiting embeddings of Besov spaces
Volume 171 / 2005
Studia Mathematica 171 (2005), 1-13
MSC: 46E30, 46E35.
DOI: 10.4064/sm171-1-1
Abstract
We investigate the classical embedding $B_{p,\theta }^s\subset B_{q,\theta }^{s-n(1/p-1/q)}$. The sharp asymptotic behaviour as $s\to 1$ 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.
