Optimal Hardy Inequality for Fractional Laplacians on the Integers

TL;DR

This paper investigates the fractional Hardy inequality on the integers, establishing the optimal Hardy weight and confirming the sharpness of the inequality's constant.

Contribution

It provides the first proof of the optimal Hardy weight for fractional Laplacians on the integers, demonstrating the inequality's sharpness.

Findings

Proved the optimality of the Hardy weight for fractional Laplacians on integers.

Confirmed the sharpness of the Hardy inequality constant.

Established foundational results for fractional inequalities on discrete domains.

Abstract

We study the fractional Hardy inequality on the integers. We prove the optimality of the Hardy weight and hence affirmatively answer the question of sharpness of the constant.