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.