What question did this study set out to answer?

The central aim is to establish a new trigonometric-Hardy-Hilbert integral inequality using a cosine-difference kernel function.

April 1, 2026Fundamental Journal of Mathematics and Applications0 citationsOpen Access

On a Trigonometric-Hardy-Hilbert Integral Inequality Based on a Cosine-Difference Kernel Function

CCChristophe ChesneauNormandie Université

Key Points

The central aim is to establish a new trigonometric-Hardy-Hilbert integral inequality using a cosine-difference kernel function.
Developed a new integral inequality based on a cosine-difference kernel function.
Utilized variable changes to support the proof.
Exploited a variation of the Hardy-Hilbert integral inequality.
A sharp constant factor was identified in the new inequality.
Two supplementary integral inequalities were derived, showcasing the main result's usability.

Abstract

This article establishes a new trigonometric-Hardy-Hilbert-type integral inequality involving a cosine-difference kernel function. The proof relies on several changes of variables and a well-known variation of the Hardy-Hilbert integral inequality. A sharp constant factor is obtained. Two additional integral inequalities are presented to demonstrate the applicability of the main result.

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