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Little Hankel operators and associated integral inequalities. (English) Zbl 1338.47023
Summary: 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.
##### MSC:
 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators 47B38 Linear operators on function spaces (general) 26D15 Inequalities for sums, series and integrals
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