Geodesic
Entropy numbers of embeddings of Sobolev spaces in Zygmund spaces
Studia Mathematica, Tome 128 (1998) no. 1, pp. 71-102

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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.
DOI : 10.4064/sm-128-1-71-102

D. E. Edmunds 1

1 
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D. E. Edmunds. Entropy numbers of embeddings of Sobolev spaces in Zygmund spaces. Studia Mathematica, Tome 128 (1998) no. 1, pp. 71-102. doi: 10.4064/sm-128-1-71-102

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