On limiting embeddings of Besov spaces

V. I. Kolyada¹ ; A. K. Lerner²

¹ Department of Mathematics Karlstad University 651 88 Karlstad, Sweden
² Department of Mathematics Bar-Ilan University 52900 Ramat Gan, Israel

Studia Mathematica, Tome 171 (2005) no. 1, pp. 1-13

Résumé

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.

Détail

DOI : 10.4064/sm171-1-1

Keywords: investigate classical embedding theta subset theta s n p sharp asymptotic behaviour operator norm embedding found particular result yields refinement bourgain brezis mironescu theorem concerning analogous problem sobolev type embedding different elementary proof latter theorem