First version: How to calculate the inverse Fourier transform of $\exp(-k a^2)/k^2$ with $k = \sqrt{k_1^2+k_2^2}$ and a parameter $a$ ? Thank you. I have no idea for this.
Second version: I means to calculate the following integral $$ \int\limits_{-\infty }^{\infty } \int\limits_{-\infty }^{\infty } \mathrm{exp} (-i k_1 x_1 - i k_2 x_2) \mathrm{exp} (-a^2\sqrt{{k_1}^2+{k_2}^2} )/({k_1}^2+{k_2}^2) \mathrm{d} k_1 \mathrm{d} k_2 $$ Many thanks for the comments and help! (I have learned how to input formulas using Latex (https://www.latexlive.com/) now, sorry for the ambiguous first version)