Skip to content Skip to navigation

Little Hankel Operators and Associated Integral Inequalities

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

Little Hankel Operators and Associated Integral Inequalities

Price: $20.00

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.