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.