Table of Content
Hardy-Hilbert-type integral inequalities
Open AccessArticleOn Five Original Integral Inequalities of the Hardy-Hilbert Type
Christophe Chesneau
Annals of Communications in Mathematics 2025,
8 (4),
431-441
DOI: https://doi.org/10.62072/acm.2025.080401
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.
Open AccessArticleExtending and unifying Hardy-Hilbert-type integral inequalities involving primitives
Christophe Chesneau
Annals of Communications in Mathematics 2026,
9(1),
12
DOI: https://doi.org/10.62072/acm.2026.09012
Abstract. In this article, we extend and unify the framework of a modified Hardy-Hilbert-type integral inequality established by W. T. Sulaiman in 2010. Our approach differs from previous works by incorporating the primitives of the main functions, considering four types of denominators for the kernel function, and introducing four adjustable parameters. The proofs are presented in full detail and can be reproduced with only a minimal level of prior knowledge.