Dispersive type estimates for Fourier integrals and applications to hyperbolic systems

Abstract

In this note we provide dispersive estimates for Fourier integrals with parameter-dependent phase functions in terms of geometric quantities of associated families of Fresnel surfaces. The results are based on a multidimensional van der Corput lemma due to the first author.Applications to dispersive estimates for hyperbolic systems and scalar higher order hyperbolic equations are also discussed.