\({L^p - L^q}\) decay estimates for Klein-Gordon models with effective mass (Q380614)

Summary: The goal of this paper is to derive \(L^p - L^q\) decay estimates for Klein-Gordon 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.