Riesz kernel
= Riesz kernel
The locally integrable homogeneous function $x\mapsto|x|^{-\alpha}$, $0<\alpha<n$, is a Riesz kernel. For $\widehat f(\xi)=\int e^{-ix\cdot\xi}f(x)\,dx$,
$$
\widehat{|x|^{-\alpha}}(\xi)
=2^{n-\alpha}\pi^{n/2}
\frac{\Gamma((n-\alpha)/2)}{\Gamma(\alpha/2)}
|\xi|^{\alpha-n}.
$$