On the Hubert Inequality

Abstract

It is shown that the Hilbert inequality for double series can be improved by introducing the positive real number 1 r(j + where s(x) = > I' 'and IxII2 x, (x = a, b). The coefficient ir of the classical Hilbert inequality is proved not to be the best possible if h a il or il bil is finite. A similar result for the Hubert integral inequality is also proved.