Entropy and approximation numbers of embeddings between weighted Besov spaces

• Autorzy: Iwona Piotrowska
• Języki publikacji: EN

Abstrakty

EN

The present paper is devoted to the study of the "quality" of the compactness of the trace operator. More precisely, we characterize the asymptotic behaviour of entropy numbers of the compact map
$tr_{Γ}: B^{s}_{p₁,q} (ℝⁿ,w_{ϰ}^{Γ}) → L_{p₂}(Γ)$,
where Γ is a d-set with 0 < d < n and $w_{ϰ}^{Γ}$ a weight of type $w_{ϰ}^{Γ}(x) ~ dist(x,Γ)^{ϰ}$ near Γ with ϰ > -(n-d). There are parallel results for approximation numbers.

Kategorie tematyczne

• 42B35: Function spaces arising in harmonic analysis
• 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

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2008
• Tom: 79
• Numer: 1
• Strony: 173-185

Daty

wydano

2008

Twórcy

autor

Iwona Piotrowska

• Mathematical Institute, Friedrich-Schiller-University, Ernst-Abbe-Platz 2, 07737 Jena, Germany

Identyfikatory

DOI

10.4064/bc79-0-14