Norm of the Hilbert matrix on Bergman spaces

被引：19

作者：

Bozin, Vladimir ^{[1
]}

Karapetrovic, Boban ^{[1
]}

机构：

[1] Univ Belgrade, Fac Math, Studentski Trg 16, Belgrade, Serbia

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2018年 / 274卷 / 02期

关键词：

Hilbert matrix; Bergman spaces; OPERATORS;

D O I：

10.1016/j.jfa.2017.08.005

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is well known that the Hilbert matrix, operator H is a bounded operator from the Bergman space A(P) into A(P) if and only if 2 < p < infinity. In [5] it was shown that the norm of the Hilbert matrix operator H on the Bergman space A(P) is equal to pi/sin2 pi/p when 4 <= p < infinity, and it was also conjectured that parallel to H parallel to(Ap -> Ap) = pi/sin2 pi/p, when 2 < p < 4. In this paper we prove this conjecture. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：525 / 543

页数：19

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