## Communications in Mathematical Analysis

### Little Hankel Operators and Associated Integral Inequalities

#### 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