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# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## On limiting embeddings of Besov spaces

### Tom 171 / 2005

Studia Mathematica 171 (2005), 1-13 MSC: 46E30, 46E35. DOI: 10.4064/sm171-1-1

#### Streszczenie

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.