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Abstract

The present paper is devoted to the study of the “quality” of the compactness of the trace operator. More precisely, we characterize the asymptotic behaviour of entropy numbers of the compact map $$ {\rm tr}_{\Gamma}:\;B^{s}_{p_1,q}(\mathbb{R}^n,w_{\varkappa }^{\Gamma})\longrightarrow L_{p_2}(\Gamma), $$ where $\Gamma$ is a $d$-set with $0< d< n$ and $w_{\varkappa}^{\Gamma}$ a weight of type $w_{\varkappa}^{\Gamma}(x)\sim \mathop{\rm dist}(x,\Gamma)^{\varkappa}$ near $\Gamma$ with $\varkappa > -(n-d)$. There are parallel results for approximation numbers.