Entropy and approximation numbers of weighted Sobolev spaces via bracketing

We investigate the asymptotic behaviour of entropy and approximation numbers of the compact embedding $E_{p,\sigma }^m(B)\hookrightarrow L_p(B)$, $1\leq p<\infty,$definedontheunitball$B$in$$\mathbb{R}$^n$\mathrm{.}Here$E^m_{p,\sigma}(B)$ 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, we apply a bracketing technique which is an analogue to that of Dirichlet-Neumann-bracketing used by Triebel if $p=2$.