Determination of the Best Constant in an Inequality of Hardy, Littlewood, and Pólya

Abstract

In 1934 Hardy, Littlewood, and Pólya generalized Hilbert's inequality to the case in which the parameters are not conjugate. Determination of the best constant in this generalization is still an unsolved problem. An experimental approach is presented that yields numerical values that agree with theory in the cases in which an exact answer is known. The results may be a guide to a further theoretical approach.