In this work dispersive and Strichartz estimates for solutions to general strictly hyperbolic partial differential equations with constant coefficients with lower order terms are considered. The global time decay estimates of Lp–Lq norms of propagators are analysed in detail and it is described how the time decay rates depend on the geometry of the problem. For these purposes, the frequency space is separated in several zones each giving a certain decay rate. Geometric conditions on characteristics responsible for the particular decay are presented.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets