Multidimensional Frank-Laptev-Weidl improvement of the Hardy Inequality

TL;DR

This paper introduces a novel multidimensional improvement of the classical Hardy inequality in the supercritical case, utilizing radialisation and rearrangement techniques to extend recent one-dimensional developments.

Contribution

It presents a new multidimensional Hardy inequality improvement based on radialisation and rearrangement methods, advancing the understanding of Hardy inequalities in higher dimensions.

Findings

New multidimensional Hardy inequality established

Uses radialisation and rearrangement techniques

Discusses implications and consequences

Abstract

We establish a new improvement of the classical $L^p$-Hardy inequality on the multidimensional Euclidean space in the supercritical case. Recently, in [14], there has been a new kind of development of the one dimensional Hardy inequality. Using some radialisation techniques of functions and then exploiting symmetric decreasing rearrangement arguments on the real line, the new multidimensional version of the Hardy inequality is given. Some consequences are also discussed.