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1998 | 128 | 1 | 71-102

Tytuł artykułu

Entropy numbers of embeddings of Sobolev spaces in Zygmund spaces

Treść / Zawartość

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.

Twórcy

  • School of Mathematical Sciences, University of Sussex, Falmer, Brighton BN1 9QHi, U.K.
autor
  • King's College London, Strand, London WC2R 2LS, U.K.

Bibliografia

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  • [BiS2] M. S. Birman and M. Z. Solomyak, Estimates for the number of negative eigenvalues of the Schrödinger operator and its generalizations, in: Adv. Soviet Math. 7, Amer. Math. Soc., 1991, 1-55.
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