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Open Journal of Mathematical Sciences (OMS)

ISSN: 2523-0212 (Online) 2616-4906 (Print)
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  • Research article

On several arctangent- and logarithmic-Hardy-Hilbert integral inequalities

Christophe Chesneau1
1Department of Mathematics, LMNO, University of Caen-Normandie, 14032 Caen, France
Copyright © Christophe Chesneau. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
  • Received: 09/10/2025
  • Accepted: 30/12/2025
  • Published: 19/01/2026

Abstract

In this paper, we establish several new arctangent- and logarithmic-Hardy-Hilbert integral inequalities. The approach combines fundamental principles with refined techniques from the theory of integral inequalities, leading to a range of original results. Complete proofs are presented together with a discussion of their sharpness and potential applications.

Keywords: Hardy-Hilbert integral inequality, arctangent function, logarithmic function, weighted \(L^p\) norm