On Some Connections Between Hilbert and Hardy Type Integral Inequalities

This article investigates some new connections between the Hilbert and Hardy integral inequalities. In particular, two general theorems are established, both based on integral terms derived from those used in these two famous inequalities. They have the property of depending on two functions and one modulable parameter. Applications and examples are given to specific cases combining Hilbert and Hardy type integral inequalities. Emphasis is placed on a particular weighted integral term, showing how our results can be used to improve what can be obtained with some classical integral inequalities in the literature.