On limiting embeddings of Besov spaces

V. I. Kolyada; A. K. Lerner

Studia Mathematica, Tome 166 (2005), p. 1-13 / Harvested from The Polish Digital Mathematics Library

Résumé

We investigate the classical embedding $B_{p, θ}^{s} \subset B_{q, θ}^{s - n (1 / p - 1 / q)}$ . 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.

Publié le : 2005-01-01

Zbl 1090.46026

EUDML-ID : urn:eudml:doc:284640

@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm171-1-1,
     author = {V. I. Kolyada and A. K. Lerner},
     title = {On limiting embeddings of Besov spaces},
     journal = {Studia Mathematica},
     volume = {166},
     year = {2005},
     pages = {1-13},
     zbl = {1090.46026},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm171-1-1}
}

V. I. Kolyada; A. K. Lerner. On limiting embeddings of Besov spaces. Studia Mathematica, Tome 166 (2005) pp. 1-13. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm171-1-1/