The best constant in a fractional Hardy inequality

TL;DR

This paper establishes an optimal Hardy inequality for the fractional Laplacian operator in the half-space, providing a fundamental mathematical result with potential implications for analysis and PDEs.

Contribution

It introduces the best constant in a fractional Hardy inequality specifically for the half-space, advancing the understanding of fractional operators.

Findings

Derived the optimal constant for the fractional Hardy inequality

Extended classical Hardy inequalities to fractional Laplacians

Provided a rigorous proof for the inequality in the half-space

Abstract

We prove an optimal Hardy inequality for the fractional Laplacian on the half-space.