On new generalizations of Hilbert's inequality and their applications
Inequalities for a general series of type \(\sum^{+\infty}_{m=0} \sum^{+\infty}_{n=0} K(m+ t,n+t) a_mb_n\) are proved. For particular \(K\), the authors obtain refinements of certain inequalities related to Hilbert's inequality, due, e.g., to Hardy-Littlewood-Pólya, M. Z. Gao or J. W. S. Cassels, etc.
scientific article; zbMATH DE number 1449175