Entropy numbers of embeddings of Sobolev spaces in Zygmund spaces

• Autorzy: D. E. Edmunds , Yu. Netrusov
• Języki publikacji: EN

Abstrakty

EN

Let id be the natural embedding of the Sobolev space $W_p^l(Ω)$ in the Zygmund space $L_q(log L)_a(Ω)$, 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 $e_k(id)$ of this embedding and show that $e_k(id) ≍ k^{-η}$, 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.

Kategorie tematyczne

• 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
• 41A46: Approximation by arbitrary nonlinear expressions; widths and entropy

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1998
• Tom: 128
• Numer: 1
• Strony: 71-102

Daty

wydano

1998

otrzymano

1997-07-07

Twórcy

autor

D. E. Edmunds

• School of Mathematical Sciences, University of Sussex, Falmer, Brighton BN1 9QHi, U.K.

autor

Yu. Netrusov

• King's College London, Strand, London WC2R 2LS, U.K.

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