Factorization of entropy ideals: proportional case

Castillo, Jesús M.F.

Displaying similar documents to “Factorization of entropy ideals: proportional case”

Proportional factorization of entropy ideals.

Jesús M. Fernández Castillo (1990)

Extracta Mathematicae

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Entropy numbers of r-nuclear operators in Banach spaces of type q

Thomas Kühn (1984)

Studia Mathematica

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Entropy numbers of embeddings of Sobolev spaces in Zygmund spaces

D. Edmunds, Yu. Netrusov (1998)

Studia Mathematica

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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.