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

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.