While working on a proof of Biot-Savart law in three dimensions (2D case, though simpler, should be provable in a similar manner) - if $curl \ (v) = \omega$ then $v=\int K(x-y) \omega(y,t) dy$, where $K(x)\omega=\frac{1}{4 \pi} \frac{x \times \omega}{|x|^3}$ ) I came across the following function for which I want to find the inverse fourier transform:
$$\frac{w_3}{w^2_1+w^2_2+w^2_3}$$
I haven't studied multi-dimensional fourier transforms and mathematica doesn't return any results. Any tips on how to find the transform?