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.
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
Affiliations des auteurs :
V. I. Kolyada
1
;
A. K. Lerner
2
1
Department of Mathematics Karlstad University 651 88 Karlstad, Sweden
2
Department of Mathematics Bar-Ilan University 52900 Ramat Gan, Israel
@article{10_4064_sm171_1_1,
author = {V. I. Kolyada and A. K. Lerner},
title = {On limiting embeddings of {Besov} spaces},
journal = {Studia Mathematica},
pages = {1--13},
year = {2005},
volume = {171},
number = {1},
doi = {10.4064/sm171-1-1},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm171-1-1/}
}
TY - JOUR
AU - V. I. Kolyada
AU - A. K. Lerner
TI - On limiting embeddings of Besov spaces
JO - Studia Mathematica
PY - 2005
SP - 1
EP - 13
VL - 171
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.4064/sm171-1-1/
DO - 10.4064/sm171-1-1
LA - en
ID - 10_4064_sm171_1_1
ER -
%0 Journal Article
%A V. I. Kolyada
%A A. K. Lerner
%T On limiting embeddings of Besov spaces
%J Studia Mathematica
%D 2005
%P 1-13
%V 171
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4064/sm171-1-1/
%R 10.4064/sm171-1-1
%G en
%F 10_4064_sm171_1_1
V. I. Kolyada; A. K. Lerner. On limiting embeddings of Besov spaces. Studia Mathematica, Tome 171 (2005) no. 1, pp. 1-13. doi: 10.4064/sm171-1-1
