Entropy and Approximation Numbers of Embeddings of Function Spaces with Muckenhoupt Weights, I

Abstract

We study compact embeddings for weighted spaces of Besov and Triebel-Lizorkin type where the weight belongs to some Muckenhoupt Ap class. For weights of purely polynomial growth, both near some singular point and at infinity, we obtain sharp asymptotic estimates for the entropy numbers and approximation numbers of this embedding. The main tool is a discretization in terms of wavelet bases.