Bernstein n-Widths of Besov Embeddings on Lipschitz Domains  

作　　者：Yue Wu LI Gen Sun FANG 

机构地区：[1]School of Mathematical Sciences, Hulunbeier University [2]School of Mathematical Sciences, Beijing Normal University

出　　处：《Acta Mathematica Sinica,English Series》2013年第12期2283-2294,共12页数学学报（英文版）

基　　金：supported by Natural Science Foundation of Inner Mongolia(Grant No.2011MS0103);supported by National Natural Science Foundation of China(Grant No.10671019)

摘　　要：In this paper, using an equivalent characterization of the Besov space by its wavelet coefficients and the discretization technique due to Maiorov, we determine the asymptotic degree of the Bernstein n-widths of the compact embeddings Bq0s＋t（Lp0（Ω））→Bq1s（Lp1（Ω））, t〉max{d（1/p0-1/p1）, 0}, 1 ≤ p0, p1, q0, q1 ≤∞,where Bq0s＋t（Lp0（Ω）） is a Besov space defined on the bounded Lipschitz domain Ω ？ Rd. The results we obtained here are just dual to the known results of Kolmogorov widths on the related classes of functions.In this paper, using an equivalent characterization of the Besov space by its wavelet coefficients and the discretization technique due to Maiorov, we determine the asymptotic degree of the Bernstein n-widths of the compact embeddings Bq0s＋t（Lp0（Ω））→Bq1s（Lp1（Ω））, t〉max{d（1/p0-1/p1）, 0}, 1 ≤ p0, p1, q0, q1 ≤∞,where Bq0s＋t（Lp0（Ω）） is a Besov space defined on the bounded Lipschitz domain Ω ？ Rd. The results we obtained here are just dual to the known results of Kolmogorov widths on the related classes of functions.

关 键 词：Bernstein widths Besov spaces Lipschitz domains 

分 类 号：O174[理学—数学]