On a Sine-Hardy–Hilbert Integral Inequality

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.