Norm of the Hilbert matrix on Bergman and Hardy spaces and a theorem of Nehari type

被引：38
|
作者：
Dostanic, Milutin [3 ]
Jevtic, Miroljub [3 ]
Vukotic, Dragan [1 ,2 ]
机构：
[1] Univ Autonoma Madrid, Dept Matemat, E-28049 Madrid, Spain
[2] Matemat Fak, Belgrade 11000, Serbia
[3] Matemat Fak, Belgrade 11000, Serbia
来源：
JOURNAL OF FUNCTIONAL ANALYSIS | 2008年 / 254卷 / 11期
关键词：
Hilbert matrix; operator norm; Hardy spaces; Bergman spaces; Hankel operator; Nehari theorem;
D O I：
10.1016/j.jfa.2008.02.009
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The Hilbert matrix induces a bounded operator on most Hardy and Bergman spaces, as was shown by Diamantopoulos and Siskakis. We generalize this for any Hankel operator on Hardy spaces by using a result of Hollenbeck and Verbitsky on the Riesz projection and also compute the exact value of the norm of the Hilbert matrix. Using a new technique, we determine the norm of the Hilbert matrix on a wide range of Bergman spaces. (c) 2008 Elsevier Inc. All rights reserved.
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页码：2800 / 2815
页数：16
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