OSCILLATORY INTEGRALS WITH NONHOMOGENEOUS PHASE FUNCTIONS RELATED TO SCHR ¨ODINGER EQUATIONS

ABSTRACT. In this paper we consider solutions to the free Schrödinger equation in n + 1 dimensions. When we restrict the last variable to be a smooth function of the first n variables we find that the solution, so restricted, is locally in L2, when the initial data is in an appropriate Sobolev space