L-p - L-q decay estimates for Klein-Gordon models with effective mass

The goal of this paper is to derive L-p - L-q decay estimates for KleinGordon models with an effective mass. We explain first the WKB analysis which leads to a representation of the solution by Fourier multipliers. Then we use stationary phase method to get L-p - L-q decay estimates on the conjugate line. The effective mass allows to derive a Klein-Gordon type decay rate. Some comments to L-p - L-q decay rates for scale-invariant models and for Klein-Gordon models possessing scattering states to wave models complete the paper.