On limiting embeddings of Besov spaces

V. I. Kolyada, and A. K. Lerner. "On limiting embeddings of Besov spaces." Studia Mathematica 171.1 (2005): 1-13. <http://eudml.org/doc/284640>.

@article{V2005,
abstract = {We investigate the classical embedding $B_\{p,θ\}^\{s\} ⊂ B_\{q,θ\}^\{s-n(1/p-1/q)\}$. 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.},
author = {V. I. Kolyada, A. K. Lerner},
journal = {Studia Mathematica},
keywords = {Sobolev space; Besov space; embedding theorem; rearrangement estimate; modulus of continuity},
language = {eng},
number = {1},
pages = {1-13},
title = {On limiting embeddings of Besov spaces},
url = {http://eudml.org/doc/284640},
volume = {171},
year = {2005},
}

TY - JOUR
AU - V. I. Kolyada
AU - A. K. Lerner
TI - On limiting embeddings of Besov spaces
JO - Studia Mathematica
PY - 2005
VL - 171
IS - 1
SP - 1
EP - 13
AB - We investigate the classical embedding $B_{p,θ}^{s} ⊂ B_{q,θ}^{s-n(1/p-1/q)}$. 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.
LA - eng
KW - Sobolev space; Besov space; embedding theorem; rearrangement estimate; modulus of continuity
UR - http://eudml.org/doc/284640
ER -