Self-improvement of pointwise Hardy inequality

TL;DR

This paper proves that a specific mathematical inequality, the pointwise p-Hardy inequality, can be improved upon itself using advanced techniques involving maximal functions and curve characterizations.

Contribution

It introduces a novel proof demonstrating the self-improvement property of the pointwise p-Hardy inequality using maximal function methods and curve-based characterizations.

Findings

Established the self-improvement property of the pointwise p-Hardy inequality.

Utilized maximal function techniques in the proof.

Characterized the inequality through curves.

Abstract

We prove the self-improvement of a pointwise $p$-Hardy inequality. The proof relies on maximal function techniques and a characterization of the inequality by curves.