Sampling Numbers and Embedding Constants

H. Triebel

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Studies on function theory and differential equations, Tome 248 (2005), pp. 275-284

Résumé

The paper deals with the spaces $G_1(\Omega)=A^s_{pq}(\Omega)$ of Sobolev–Besov type in bounded Lipschitz domains $\Omega$ in $\mathbb R^n$ such that $G_1(\Omega)$ is compactly embedded in $C(\overline{\Omega})$. Sampling numbers measure the accuracy of the recovery of $f \in G_1(\Omega)$ in diverse target spaces $G_2(\Omega)$ of the same type. We prove equivalence assertions for these numbers and study what happens in limiting situations.