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Almost optimal estimates for entropy numbers of B 2,2 1/2 and its consequences

Almost optimal estimates for entropy numbers of B 2,2 1/2 and its consequences Triebel’s conjecture on the entropy numbers for the limiting embedding case B p , p 1/ p ↪ E ν, E ν being suitable Orlicz spaces, is almost proved for p≥2 – almost in the sense that a log -factor occurs in the upper estimate. Furthermore, it is shown that the “breaking point”, where the radii of the ɛ-balls in the covering of the B p , q 1/ p -unit ball stop to be constant, essentially depends on the second parameter q. The methods used in the paper also give improvements of the results till now known in the case p<2, explains a result of Kashin and Temlyakov on entropy numbers of continuous functions of low smoothness, and indicates how the E ν -scale can be refined. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematische Zeitschrift Springer Journals

Almost optimal estimates for entropy numbers of B 2,2 1/2 and its consequences

Belinsky, E.; Trebels, W.
Mathematische Zeitschrift , Volume 250 (1) – Oct 21, 2004
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References (16)

Publisher
Springer Journals
Copyright
Copyright © 2004 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Mathematics, general
ISSN
0025-5874
eISSN
1432-1823
DOI
10.1007/s00209-004-0734-0
Publisher site
See Article on Publisher Site

Abstract

Triebel’s conjecture on the entropy numbers for the limiting embedding case B p , p 1/ p ↪ E ν, E ν being suitable Orlicz spaces, is almost proved for p≥2 – almost in the sense that a log -factor occurs in the upper estimate. Furthermore, it is shown that the “breaking point”, where the radii of the ɛ-balls in the covering of the B p , q 1/ p -unit ball stop to be constant, essentially depends on the second parameter q. The methods used in the paper also give improvements of the results till now known in the case p<2, explains a result of Kashin and Temlyakov on entropy numbers of continuous functions of low smoothness, and indicates how the E ν -scale can be refined.

Journal

Mathematische Zeitschrift – Springer Journals

Published: Oct 21, 2004

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