Entropy and approximation numbers of weighted Sobolev spaces via bracketing

We investigate the asymptotic behaviour of entropy and approximation numbers of the compact embedding id : E-p,sigma(m)(B) -> L-p(B), 1 <= p < infinity, defined on the unit ball B in R-n. Here E-p,sigma(m)(B) denotes a Sobolev space with a power weight perturbed by a logarithmic function. The weight contains a singularity at the origin. Inspired by Evans and Harris [5], we apply a bracketing technique which is an analogue to that of Dirichlet-Neumann bracketing used by Triebel in [14] for p= 2. (C) 2016 Elsevier Inc. All rights reserved.