Entropy Numbers of Sequence Space Embeddings, and Applications to Function Spaces
by
Thomas Kühn
Universität Leipzig

Several new estimates for entropy numbers of certain sequence space embeddings are established, e.g. the lower estimate

ek(id : lpn --> lqn) >= c (log(1+n/k)/k)1/p-1/q

for arbitrary 0 < p < q < \infty, n in N and logn <= k <= n , where the constant c is independent on n and k. In the quasi-Banach case, 0 < p < 1, for such `medium size' k's so far only an upper estimate has been known.

Other results concern weighted (quasi-)Banach sequence spaces with mixed norms. As an application upper entropy estimates for embeddings of Besov function spaces in Lipschitz type spaces are obtained, thus improving earlier results by Edmunds and Haroske.

Date received: February 22, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafv-36.