Asia Mathematika, Vol 9, issue 2, pages: 51-62.

Statement and proof of a new general Hardy-Hilbert-type integral inequality theorem

Christophe Chesneau
Department of Mathematics, LMNO, University of Caen-Normandie, Caen, France.

Received: 08 Jul 2025 | Accepted: 21 Jul 2025 | Final Version: 31 Aug 2025

Abstract

In this study, we establish a theorem that provides a new type of Hardy-Hilbert-type integral inequality. It has the characteristic of being very general and flexible, using a special primitive-type operator, four intermediate functions and seven adaptable parameters. The corresponding proof has the originality of combining a new integral result and "old" Hardy integral inequalities, which merge thanks to appropriate choices of the parameters. Several examples are provided to demonstrate how the theorem can be applied in certain tractable settings.

Keywords:
Hardy integral inequality, Hilbert integral inequality, H\"older integral inequality.

1. Introduction

Hardy-Hilbert-type integral inequalities have always been of great interest in mathematical analysis. The formal statements of two key inequalities...

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