A Multiparameter Hardy–Hilbert-Type Inequality Containing Partial Sums as the Terms of Series

Abstract

In this study, a multiparameter Hardy–Hilbert-type inequality for double series is established, which contains partial sums as the terms of one of the series. Based on the obtained inequality, we discuss the equivalent statements of the best possible constant factor related to several parameters. Moreover, we illustrate how the inequality obtained can generate some new Hardy–Hilbert-type inequalities.