We consider the scattering map introduced by Beals and Coifman and Fokas and Ablowitz that may be used to transform one of the Davey Stewartson equations to a linear evolution. We give mapping properties of the scattering transform on weighted L^2  Sobolev spaces that mimic well-known properties of the Fourier transform. This is joint work with  Katharine Ott, Peter Perry, and Nathan Serpico.