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:Ep,σm(B)↪Lp(B), 1≤p<∞1≤p<∞, defined on the unit ball B   in RnRn. Here Ep,σm(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=2p=2.