Statement and proof of a new general Hardy-Hilbert-type integral inequality theorem

In this study, we establish a theorem that provides a new type of Hardy-Hilbert-type integral inequality. It has the characteristic of being very general and flexible, using a special primitive-type operator, four intermediate functions and seven adaptable parameters. The corresponding proof has the originality of combining a new integral result and "old" Hardy integral inequalities, which merge thanks to appropriate choices of the parameters. Several examples are provided to demonstrate how the theorem can be applied in certain tractable settings.