Some s-numbers of an integral operator of Hardy type in Banach function spaces

被引：0

作者：

Edmunds, David ^{[1
]}

Gogatishvili, Amiran ^{[2
]}

Kopaliani, Tengiz ^{[3
]}

Samashvili, Nino ^{[3
]}

机构：

[1] Univ Sussex, Dept Math, Pevensey 2,North South Rd, Brighton BN1 9QH, E Sussex, England

[2] Acad Sci Czech Republ, Inst Math, Zitna 25, CR-11567 Prague 1, Czech Republic

[3] I Javakhishvili Tbilisi State Univ, Fac Exact & Nat Sci, Univ St 2, GE-0143 Tbilisi, Georgia

来源：

JOURNAL OF APPROXIMATION THEORY | 2016年 / 207卷

基金：

美国国家科学基金会;

关键词：

Hardy type operators; Banach function spaces; s-numbers; Compact linear operators; APPROXIMATION NUMBERS; WIDTHS;

D O I：

10.1016/j.jat.2016.02.003

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let s(n)(T) denote the nth approximation, isomorphism, Gelfand, Kolmogorov or Bernstein number of the Hardy-type integral operator T given by T f(x) = v(x) integral(x)(a) u(t) f(t)dt, x is an element of (a, b) (-infinity < a < b < +infinity) and mapping a Banach function space E to itself. We investigate some geometrical properties of E for which C-1 integral(b)(a) u(x)v(x)dx <= lim(n ->infinity) inf ns(n) (T) <= lim(n ->infinity)sup ns(n)(T) <= C-2 integral(b)(a) u(x)v(x)dx under appropriate conditions on it and v. The constants C-1, C-2 > 0 depend only on the space E. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：76 / 97

页数：22

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