Entropy and approximation numbers of embeddings between weighted Besov spaces
Tom 79 / 2008
Banach Center Publications 79 (2008), 173-185
MSC: Primary 46E35; Secondary 42B35, 47B06.
DOI: 10.4064/bc79-0-14
Streszczenie
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.
