We prove sharp embeddings of Besov spaces Bp,r σ,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.
@article{urn:eudml:doc:44545,
title = {Sharp embeddings of Besov spaces with logarithmic smoothness.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {18},
year = {2005},
pages = {81-110},
zbl = {1083.46018},
mrnumber = {MR2135533},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44545}
}
Gurka, Petr; Opic, Bohumir. Sharp embeddings of Besov spaces with logarithmic smoothness.. Revista Matemática de la Universidad Complutense de Madrid, Tome 18 (2005) pp. 81-110. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44545/