# Integral representation using Green function for fractional Hardy equation

## TL;DR

This paper investigates the Green function for a fractional Hardy operator, establishing an integral representation for weak solutions and advancing understanding of fractional Hardy equations.

## Contribution

It introduces a Green function framework for the fractional Hardy operator and demonstrates the integral representation of weak solutions, a novel approach in this context.

## Key findings

- Derived the Green function for the fractional Hardy operator
- Proved the integral representation formula for weak solutions
- Enhanced theoretical understanding of fractional Hardy equations

## Abstract

Our main aim is to study Green function for the fractional Hardy operator $P:=(-\Delta)^s -\frac{\theta}{|x|^{2s}}$ in $\mathbb{R}^N$, where $0<\theta<\Lambda_{N,s}$ and $\Lambda_{N,s}$ is the best constant in the fractional Hardy inequality. Using Green function, we also show that the integral representation of the weak solution holds.