Improvement of the discrete Hardy inequality

TL;DR

This paper presents a new enhancement of the classical discrete Hardy inequality, extending recent continuous inequalities through weighted inequalities and discrete rearrangement techniques.

Contribution

It introduces a novel improvement of the discrete Hardy inequality using weighted inequalities and discrete rearrangement methods, bridging continuous and discrete cases.

Findings

New improved discrete Hardy inequality established

Uses weighted inequalities and rearrangement techniques

Connects discrete and continuous inequality results

Abstract

We establish a novel improvement of the classical discrete Hardy inequality, which gives the discrete version of a recent (continuous) inequality of Frank, Laptev, and Weidl. Our arguments build on certain weighted inequalities based on discrete analogues of symmetric decreasing rearrangement techniques.