  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.
