I'm trying to do a Fourier transform of this function
$$\frac{\bigtriangleup f(\textbf{x})}{1+f(\textbf{x})}$$
in terms of $\mathcal{F}(f(\textbf{x}))$. (Just like here $\mathcal{F}\left({\bigtriangleup f(\textbf{x})}\right)=-k^2\mathcal{F}(f)$)
The only solution I see is expand the denominator as series and then use convolution theorem. After that I get a lot of integrals in the answer.
So, is there ways to get more explicit answer?