Estimating the Hardy constant of nonconcave homogenus quasideviation means

TL;DR

This paper investigates the Hardy property of a class of homogeneous quasideviation means generated by functions with specific concavity and growth conditions, providing criteria and bounds for their Hardy constants.

Contribution

It offers a complete characterization of the concave envelopes of these means and establishes new sufficient conditions for their Hardy property and bounds for their Hardy constants.

Findings

Complete determination of concave envelopes of the means

Sufficient conditions for the Hardy property

Upper estimates for Hardy constants

Abstract

In this paper, we consider homogeneous quasideviation means generated by real functions (defined on $(0,\infty)$) which are concave around the point $1$ and possess certain upper estimates near $0$ and $\infty$. It turns out that their concave envelopes can be completely determined. Using this description, we establish sufficient conditions for the Hardy property of the homogeneous quasideviation mean and we also furnish an upper estimates for its Hardy constant.