I am trying to proof the following result for a Fourier transform on distributions on $\mathbb{R}^n$:
If $a\in(0,n)$, then there exist $C(n,a)\in \mathbb{R}$ such that $$ \mathcal{F(|\cdot|^{-a})} = C(n,a) |\cdot|^{a-n}, $$ where the constant $C(n,a)$ is just depending on $n$ and $a$ only.
I tried to use the classical properties of the Fourier Transform but it does not work or does not provides me any clue.
Do you any idea how to prove it ?
Why the constant $C(n,a)$ depend just on $n$ and $a$?.