Study of Hardy-Hilbert-type integral inequalities with non-homogeneous power-max kernel functions

Hardy-Hilbert-type integral inequalities are among the classics of mathematical analysis. In particular, this includes well-known variants involving homogeneous power-max kernel functions. In this article, we extend the theory by studying the non-homogeneous case using specially designed power-max kernel functions. Additionally, we explore different integration domains to increase the flexibility of our results in a variety of mathematical contexts. We also establish several equivalences, modifications and generalizations of our main integral inequalities. The proofs are detailed and self-contained. To support the theory, we provide numerical examples together with the corresponding implementation codes for transparency and reproducibility.