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Abstract <p>In recent decades, efforts have been made to deepen our understanding of the Hardy–Hilbert integral inequality by studying various generalizations and modifications. In this article, we add some contributions to the topics by considering product variants that have not received much attention. The main result is a two-dimensional integral inequality of the Hardy–Hilbert type involving primitives of functions and products of variables. It is then extended in two different ways: parametrically by including four parameters and dimensionally by considering the third dimension. The article ends with a related but independent result: a multidimensional inequality directly related to the standard Hardy integral inequality.</p>

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Some Original Product Variants of the Hardy–Hilbert Integral Inequality

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • C. Chesneau

摘要

Abstract

In recent decades, efforts have been made to deepen our understanding of the Hardy–Hilbert integral inequality by studying various generalizations and modifications. In this article, we add some contributions to the topics by considering product variants that have not received much attention. The main result is a two-dimensional integral inequality of the Hardy–Hilbert type involving primitives of functions and products of variables. It is then extended in two different ways: parametrically by including four parameters and dimensionally by considering the third dimension. The article ends with a related but independent result: a multidimensional inequality directly related to the standard Hardy integral inequality.