Communications in Mathematical Analysis

Little Hankel Operators and Associated Integral Inequalities

Namita Das and Jittendra Kumar Behera

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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.

Article information

Source
Commun. Math. Anal., Volume 18, Number 1 (2015), 1-35.

Dates
First available in Project Euclid: 12 August 2015

Permanent link to this document
https://projecteuclid.org/euclid.cma/1439384425

Mathematical Reviews number (MathSciNet)
MR3365171

Zentralblatt MATH identifier
1338.47023

Subjects
Primary: 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15] 47B38: Operators on function spaces (general) 26D15: Inequalities for sums, series and integrals

Keywords
Bergman space right half plane little Hankel operators Bergman-Hilbert matrix Hardy-Hilbert’s integral inequality

Citation

Das, Namita; Behera, Jittendra Kumar. Little Hankel Operators and Associated Integral Inequalities. Commun. Math. Anal. 18 (2015), no. 1, 1--35. https://projecteuclid.org/euclid.cma/1439384425


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