Given a Positive Sequence ,
where the s are Real and ``square summable.''
Another Inequality known as Hilbert's applies to Nonnegative sequences and ,
unless all or all are 0. If and are Nonnegative integrable functions, then the integral
is the best possible, in the sense that counterexamples can be constructed for any
Hardy, G. H.; Littlewood, J. E.; and Pólya, G. Inequalities, 2nd ed. Cambridge,
England: Cambridge University Press, pp. 308-309, 1988.
© 1996-9 Eric W. Weisstein