Approximation numbers and entropy numbers of embeddings of fractional Besov-Sobolev spaces in Orlicz spaces. (English) Zbl 0792.46024

Triebel, Hans

Proc. Lond. Math. Soc., III. Ser. 66, No. 3, 589-618 (1993).

Let \(\Omega\) be a bounded \(C^ \infty\) domain in \(\mathbb{R}^ n\). The paper deals with the approximation numbers and entropy numbers of the compact embeddings of the limiting spaces \(H^{n/p}_ p(\Omega)\) and \(B^{n/p}_ p(\Omega)\) of Besov-Sobolev type into appropriate Orlicz spaces of Trudinger type.

Reviewer: H.Triebel (Jena)

MSC:

46E35	Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
47B06	Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
46E30	Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

Keywords:

limiting spaces of Besov-Sobolev type; approximation numbers; entropy numbers; compact embeddings; Orlicz spaces of Trudinger type