Approximation numbers in some weighted function spaces
The author studies weighted function spaces of type \(B^s_{p, q}(\mathbb{R}^n, w(x))\) and \(F^s_{p, q}(\mathbb{R}^n, w(x))\), where \(w(x)\) is a weight function of at most polynomial growth, preferably \(w(x)= (1+ |x|^2)^{\alpha/2}\) with \(\alpha\in \mathbb{R}\). The main result deals with estimates for the approximation numbers of compact embeddings between spaces of this type. Furthermore, she is concerned with the dependence of the approximation numbers \(a_k\) of compact embeddings between function spaces \(B^s_{p, q}(\Omega)\) and \(F^s_{p, q}(\Omega)\) on an underlying domain \(\Omega\).
scientific article; zbMATH DE number 810861