Contributions to three-dimensional Hardy-Hilbert-type integral inequalities

Christophe Chesneau (University of Caen Normandie)

Hilbert Journal of Mathematical Analysis
Vol. 4 No. 1 (2025): Hilbert J. Math. Anal.

This article presents new extensions of the classical Hardy-Hilbert integral inequality involving primitive functions in three dimensions. Two complementary theorems are established, each providing a sharp upper bound for triple integrals associated with distinct kernel function structures. By introducing additional parameters, the proposed results offer greater flexibility and generality in the formulation and application of these inequalities.