AbstractWe establish the sharpness of the embedding of certain Besov and Triebel-Lizorkin spaces in spaces of Lipschitz type. In particular, this proves the sharpness of the Brézis-Wainger result concerning the “almost” Lipschitz continuity of elements of the Sobolev space , where 1 < p < ∞. Upper and lower estimates are obtained for the entropy numbers of related embeddings of Besov spaces on bounded domains.
CONTENTSIntroduction...........................................................51. Preliminaries.....................................................6 Spaces on ℝⁿ......................................................6 Atomic decompositions........................................8 Spaces on domains...........................................10 Embeddings.......................................................11 Entropy numbers................................................112. Sharpness.......................................................133. Lipschitz embedding, entropy numbers...........214. Comparison with related results......................30 Embeddings.......................................................30 Entropy numbers...............................................36 Estimate from above..........................................37References.........................................................42
1991 Mathematics Subject Classification: 26A16, 46E35, 41A46, 46E15.
@book{bwmeta1.element.zamlynska-17126c89-a594-4107-82bf-95c4741d8313,
author = {Edmunds D. E. and Haroske D.},
title = {Spaces of Lipschitz type, embeddings and entropy numbers},
series = {GDML\_Books},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
address = {Warszawa},
year = {1999},
zbl = {0932.46026},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.zamlynska-17126c89-a594-4107-82bf-95c4741d8313}
}
Edmunds D. E.; Haroske D. Spaces of Lipschitz type, embeddings and entropy numbers. GDML_Books (1999), http://gdmltest.u-ga.fr/item/bwmeta1.element.zamlynska-17126c89-a594-4107-82bf-95c4741d8313/