Integral representation using Green function for fractional Hardy equation

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.

16 pages