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

被引：49

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.

引用

页码：2800 / 2815

页数：16

共 18 条

[1] TRICKS OR TREATS WITH THE HILBERT MATRIX [J].

CHOI, MD .

AMERICAN MATHEMATICAL MONTHLY, 1983, 90 (05) :301-312

[2] Composition operators and the Hilbert matrix [J].

Diamantopoulos, E ;

Siskakis, AG .

STUDIA MATHEMATICA, 2000, 140 (02) :191-198

[3] Hilbert matrix on Bergman spaces [J].

Diamantopoulos, E .

ILLINOIS JOURNAL OF MATHEMATICS, 2004, 48 (03) :1067-1078

[4]

DUREN P. L., 1970, Theory of Spaces

[5]

Duren P.L., 2004, MATH SURV MONOGR, V100

[6]

Gokhberg I., 1968, FUNKT ANAL PRIL, V2, P91

[7]

Halmos P. R., 1982, HILBERT SPACE PROBLE

[8]

Hardy Godfrey H, 1997, INEQUALITIES

[9]

HEDENMALM H, 2000, GRAD TEXTS MATH, V199

[10]

HEDLUND JH, 1969, P AM MATH SOC, V22, P20

← 1 2 →