Transference theory for the trilinear restriction estimate and an application to the quadratic NLS in 3D

In this article we develop a theory for effectively transferring trilinear restriction estimates for the Schrödinger equation to functions in a more general resolution space adapted to the Schrödinger equation. As an application we provide a global theory for the quadratic NLS in three spatial dimensions in the critical Sobolev space ${\dot{H}}^{-\frac{1}{2}}$.