Entropy numbers of embeddings of Sobolev spaces in Zygmund spaces

Edmunds, D.; Netrusov, Yu.

Studia Mathematica, Tome 129 (1998), p. 71-102 / Harvested from The Polish Digital Mathematics Library

Résumé

Let id be the natural embedding of the Sobolev space $W_{p}^{l} (Ω)$ in the Zygmund space $L_{q} {(l o g L)}_{a} (Ω)$ , where $Ω = {(0, 1)}^{n}$ , 1 < p < ∞, l ∈ ℕ, 1/p = 1/q + l/n and a < 0, a ≠ -l/n. We consider the entropy numbers $e_{k} (i d)$ of this embedding and show that $e_{k} (i d) ≍ k^{- η}$ , where η = min(-a,l/n). Extensions to more general spaces are given. The results are applied to give information about the behaviour of the eigenvalues of certain operators of elliptic type.

Publié le : 1998-01-01

Zbl 0919.46024

EUDML-ID : urn:eudml:doc:216476

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     title = {Entropy numbers of embeddings of Sobolev spaces in Zygmund spaces},
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     volume = {129},
     year = {1998},
     pages = {71-102},
     zbl = {0919.46024},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv128i1p71bwm}
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Edmunds, D.; Netrusov, Yu. Entropy numbers of embeddings of Sobolev spaces in Zygmund spaces. Studia Mathematica, Tome 129 (1998) pp. 71-102. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv128i1p71bwm/

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