The $H^p-H^q$ Estimates for a Class of Dispersive Equations with Finite Type Geometry

This paper studies the $H^p-H^q$ estimates of a class of oscillatory integrals related to dispersive equationsunder the assumption that the level hypersurfaces are convex and of finite type. As applications, we obtain the decay estimates for the solutions of higher order homogeneous and inhomogeneous Schrödinger equations.