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Home 9 Volume 9 On Five Original Integral Inequalities of the Hardy-Hilbert Type

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On Five Original Integral Inequalities of the Hardy-Hilbert Type

Christophe Chesneau^1*

Department of Mathematics, LMNO, University of Caen-Normandie, 14032 Caen, France.

* Corresponding Author: Christophe Chesneau. Email: christophe.chesneau@gmail.com

Annals of Communications in Mathematics 2025, 8 (4), 431-441. https://doi.org/10.62072/acm.2025.080401

Received: 27 September 2025 |

Accepted: 20 October 2025 |

Published: 31 December 2025

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ABSTRACT.

This article is devoted to five distinct integral inequalities of the Hardy-Hilbert type, each possessing its own originality. In particular, we highlight new trigonometric variants that yield sharp upper bounds involving weighted integral norms of the underlying functions. Complete and rigorous proofs are provided in detail.

Keywords

Hardy-Hilbert-type integral inequalities; Integral inequalities; trigonometric functions

Cite This Article

Christophe Chesneau.

On Five Original Integral Inequalities of the Hardy-Hilbert Type.

Annals of Communications in Mathematics

2025,

8 (4):

431-441.

https://doi.org/10.62072/acm.2025.080401

Creative Commons License

Copyright © 2025 by the Author(s). Licensee Techno Sky Publications. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

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