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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DOI

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. 
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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