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2015 Little Hankel Operators and Associated Integral Inequalities
Namita Das, Jittendra Kumar Behera
Commun. Math. Anal. 18(1): 1-35 (2015).

Abstract

In this paper we consider a class of integral operators on $L^2(0,\infty)$ that are unitarily equivalent to little Hankel operators between weighted Bergman spaces. We calculate the norms of such integral operators and as a by-product obtain a generalization of the Hardy-Hilbert’s integral inequality. We also consider the discrete version of the inequality which give the norms of the companion matrices of certain generalized Bergman-Hilbert matrices. These results are then generalized to vector valued case and operator valued case.

Citation

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Namita Das. Jittendra Kumar Behera. "Little Hankel Operators and Associated Integral Inequalities." Commun. Math. Anal. 18 (1) 1 - 35, 2015.

Information

Published: 2015
First available in Project Euclid: 12 August 2015

zbMATH: 1338.47023
MathSciNet: MR3365171

Subjects:
Primary: 26D15, 47B35, 47B38

Rights: Copyright © 2015 Mathematical Research Publishers

JOURNAL ARTICLE
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Vol.18 • No. 1 • 2015
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