Hardy-Hilbert type inequalities on homogeneous groups-An introduction and generalization to the kernel case

TL;DR

This paper extends Hardy-Hilbert type inequalities from classical settings to homogeneous groups, unifying various inequalities under a general kernel framework and broadening their applicability.

Contribution

It introduces Hardy-Hilbert inequalities on homogeneous groups and unifies classical inequalities into a general kernel case, generalizing to the group setting.

Findings

Unified Hardy-Hilbert inequalities with kernels

Extended inequalities to homogeneous groups

Provided a general framework for inequalities

Abstract

There is a lot of information available concerning Hardy-Hilbert type inequalities in one or more dimensions. In this paper we introduce the development of such inequalities on homogeneous groups. Moreover, we point out a unification of several of the Hardy-Hilbert type inequalities in the classical case to a general kernel case. Finally, we generalize these results to the homogeneous group case.