two dimensional extension of the Fourier transform of $|x|^\alpha$?

Question

I know the Fourier transform pair \begin{equation} |x|^\alpha \leftrightarrow -2\sin(\pi\alpha/2)\Gamma(1+\alpha)|\omega|^{-1-\alpha} \end{equation}

Can this formula be extended to two dimensional situation?

What is the Fourier transform of $|\mathbf{x}|^\alpha$($|\mathbf{x}|=\sqrt{x_1^2+x_2^2}$) ?

Thanks in advance