Nuclear Embeddings in Weighted Function Spaces

Authors:

• Dorothee D. Haroske,
• Leszek Skrzypczak

Abstract

AbstractWe study nuclear embeddings for weighted spaces of Besov and Triebel–Lizorkin type where the weight belongs to some Muckenhoupt class and is essentially of polynomial type. Here we can extend our previous results concerning the compactness of corresponding embeddings. The concept of nuclearity was introduced by A. Grothendieck in 1955. Recently there is a refreshed interest to study such questions. This led us to the investigation in the weighted setting. We obtain complete characterisations for the nuclearity of the corresponding embedding. Essential tools are a discretisation in terms of wavelet bases, operator ideal techniques, as well as a very useful result of Tong about the nuclearity of diagonal operators acting in$$\ell _p$$ℓpspaces. In that way we can further contribute to the characterisation of nuclear embeddings of function spaces on domains.