What question did this study set out to answer?

The aim is to present generalized forms of Hardy–Hilbert integral inequalities using primitives and homogeneous functions.

April 8, 2026Open Access

On new Hardy–Hilbert integral inequalities using primitives and homogeneous functions

Key Points

The aim is to present generalized forms of Hardy–Hilbert integral inequalities using primitives and homogeneous functions.
Introduced a framework allowing two parameters to vary independently.
Adjusted a homogeneity parameter for improved flexibility.
Derived sharp integral inequalities for two distinct parameter regimes.
Showcased three comprehensive applications of the main theorem.
Demonstrated improved flexibility and applicability through generalizations.
Highlighted the adaptability of the framework to various conditions.

Abstract

This article presents new generalizations of Hardy–Hilbert-type integral inequalities involving primitives and various homogeneous functions. Unlike previous results, our approach enables two parameters to vary independently and introduces an adjustable homogeneity parameter. This improves the flexibility and applicability of the framework. We derive sharp integral inequalities for two distinct parameter regimes. Three comprehensive applications are provided to emphasize the importance of our main theorem.

On new Hardy–Hilbert integral inequalities using primitives and homogeneous functions

Key Points

Abstract

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