Sharp embeddings of Besov spaces with logarithmic smoothness.

Gurka, Petr, and Opic, Bohumir. "Sharp embeddings of Besov spaces with logarithmic smoothness.." Revista Matemática Complutense 18.1 (2005): 81-110. <http://eudml.org/doc/44545>.

@article{Gurka2005,
abstract = {We prove sharp embeddings of Besov spaces Bp,rσ,α with the classical smoothness σ and a logarithmic smoothness α into Lorentz-Zygmund spaces. Our results extend those with α = 0, which have been proved by D. E. Edmunds and H. Triebel. On page 88 of their paper (Math. Nachr. 207 (1999), 79-92) they have written: ?Nevertheless a direct proof, avoiding the machinery of function spaces, would be desirable.? In our paper we give such a proof even in a more general context. We cover both the sub-limiting and the limiting cases and we determine growth envelopes of Besov spaces with logarithmic smoothness.},
author = {Gurka, Petr, Opic, Bohumir},
journal = {Revista Matemática Complutense},
keywords = {Espacios de funciones; Inmersiones e inclusiones en variedades; Espacios de Besov; Espacios de Sobolev; Recubrimientos topológicos; Operadores diferenciales; generalized Besov spaces; Lorentz–Zygmund spaces; sharp embeddings; growth envelopes},
language = {eng},
number = {1},
pages = {81-110},
title = {Sharp embeddings of Besov spaces with logarithmic smoothness.},
url = {http://eudml.org/doc/44545},
volume = {18},
year = {2005},
}

TY - JOUR
AU - Gurka, Petr
AU - Opic, Bohumir
TI - Sharp embeddings of Besov spaces with logarithmic smoothness.
JO - Revista Matemática Complutense
PY - 2005
VL - 18
IS - 1
SP - 81
EP - 110
AB - We prove sharp embeddings of Besov spaces Bp,rσ,α with the classical smoothness σ and a logarithmic smoothness α into Lorentz-Zygmund spaces. Our results extend those with α = 0, which have been proved by D. E. Edmunds and H. Triebel. On page 88 of their paper (Math. Nachr. 207 (1999), 79-92) they have written: ?Nevertheless a direct proof, avoiding the machinery of function spaces, would be desirable.? In our paper we give such a proof even in a more general context. We cover both the sub-limiting and the limiting cases and we determine growth envelopes of Besov spaces with logarithmic smoothness.
LA - eng
KW - Espacios de funciones; Inmersiones e inclusiones en variedades; Espacios de Besov; Espacios de Sobolev; Recubrimientos topológicos; Operadores diferenciales; generalized Besov spaces; Lorentz–Zygmund spaces; sharp embeddings; growth envelopes
UR - http://eudml.org/doc/44545
ER -