Estimates for n-widths of the Hardy-type operators (Addendum to "Improved estimates for the approximation numbers of the Hardy-type operators")

被引：6

作者：

Lang, J ^{[1
]}

机构：

[1] Ohio State Univ, Dept Math, Columbus, OH 43210 USA

来源：

JOURNAL OF APPROXIMATION THEORY | 2006年 / 140卷 / 02期

关键词：

approximation; Kolmogorov; Geffand and Bernstein numbers; weighted hardy-type operators; integral operators; weighted spaces;

D O I：

10.1016/j.jat.2005.11.018

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Consider the Hardy-type operator T: L-p (a, b) --> L-p (a, b), -infinity <= a< b <= infinity, which is defined by (Tf)(x) = v(x) integral(x)(a) u(t) f (t) dt. It is shown that rho(n) (T) = 1/n alpha(p) integral(b)(a) u(x)v(x) + O(n(-2)), where rho(n) (T) stands for any of the following: the Kolmogorov n-width, the Gel'fand n-width, the Bernstein n-width or the nth approximation number of T. (C) 2006 Elsevier Inc. All rights reserved.

引用

页码：141 / 146

页数：6