Spaces of Lipschitz type, embeddings and entropy numbers

Edmunds D. E., and Haroske D.. Spaces of Lipschitz type, embeddings and entropy numbers. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1999. <http://eudml.org/doc/271244>.

@book{EdmundsD1999,
abstract = {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 $H^\{1+n/p\}_p(ℝⁿ)$, 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.........................................................421991 Mathematics Subject Classification: 26A16, 46E35, 41A46, 46E15.},
author = {Edmunds D. E., Haroske D.},
keywords = {limiting embeddings; Besov spaces; fractional Sobolev spaces; compactness; entropy numbers},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {Spaces of Lipschitz type, embeddings and entropy numbers},
url = {http://eudml.org/doc/271244},
year = {1999},
}

TY - BOOK
AU - Edmunds D. E.
AU - Haroske D.
TI - Spaces of Lipschitz type, embeddings and entropy numbers
PY - 1999
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - 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 $H^{1+n/p}_p(ℝⁿ)$, 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.........................................................421991 Mathematics Subject Classification: 26A16, 46E35, 41A46, 46E15.
LA - eng
KW - limiting embeddings; Besov spaces; fractional Sobolev spaces; compactness; entropy numbers
UR - http://eudml.org/doc/271244
ER -