Dispersive type estimates for Fourier integrals and applications to hyperbolic systems
arXiv:1006.5600
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 multi-dimensional 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.
8 pages