Notes on Fourier transform and its application to three-point momentum-space integrals

The Fourier transform of two-point momentum-space Feynman integrals with massless propagators and two off-shell legs can be used to prove identities between their periods, exemplified by the glue-and-cut identity. We generalize this framework to massless momentum-space Feynman integrals with three off-shell legs and obtain a similar family of identities that can be used to calculate these integrals, especially for a non-planar subset of them, which naturally arise in the off-shell Sudakov form factors.