In "Renormalized Quantum Yang-Mills Theory on curved spacetime" it is stated on page 59 that the Fourier transformation of $\log(p^2-i0)$ is given by $-\frac{1}{2} \partial^2\left( \frac{\log(\xi^2+i0)}{\xi^2+i0}\right)$ (see (227))
I have tried several methods but I am not able to show this. Can anyone help me?