Entropy and approximation numbers of weighted Sobolev spaces via bracketing

被引：7
|
作者：
Mieth, Therese [1 ]
机构：
[1] Univ Jena, Fak Math & Informat, Inst Math, D-07737 Jena, Germany
来源：
JOURNAL OF FUNCTIONAL ANALYSIS | 2016年 / 270卷 / 11期
关键词：
Approximation numbers; Entropy numbers; Weighted Sobolev spaces; EMBEDDINGS;
D O I：
10.1016/j.jfa.2015.12.014
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
引用
收藏
页码：4322 / 4339
页数：18
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