Various forms of Hardy–Hilbert integral inequalities have been investigated in the literature. However, relatively few results concern inequalities that are defined on a bounded integration domain and involve trigonometric functions. In this article, we contribute to this area of research by presenting a new inequality closely related to the classical Hardy-Hilbert integral inequality. We discuss the sharpness of the associated constant factor. Furthermore, we apply the main result to derive two additional integral inequalities of independent interest.
C. Chesneau (2025) studied this question.