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Entropy numbers of embeddings of Sobolev spaces in Zygmund spaces

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Edmunds D. E., Netrusov Y.

Studia Mathematica

1998

tom 128

nr 1

71-102

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.

Ograniczanie wyników

1 Studia Mathematica

1 Edmunds D. E.

1 Netrusov Y.

1 1998

Wyniki wyszukiwania

Entropy numbers of embeddings of Sobolev spaces in Zygmund spaces