Let $\alpha \in (0,1)$ and $y=(y_1,y_2), y_1>1 \text{ and } y_2 \in \mathbb{R}$. How can I calculate the following integral?
$$\int_{-\infty}^{\infty}\int_{-\infty}^{-1}(-1-u_1)^{-\alpha/2}|u|^{-2}|u-y|^{-2}{\rm d}u_1{\rm d}u_2,$$
where $|\cdot|$ is the euclidean norm.
I have tried polar coordinates, but didn't work. I heard about 'subordination' but didn't really understand it. Any help is well appreciated.