Lipschitz continuity of the scattering operator for nonlinear Klein-Gordon equations

Abstract. We will give an overview of the Strichartz and Space Time Integral estimates forthe Klein-Gordon and subcritical nonlinear Klein-Gordon equations, respectively. In this frame-work, the regularity of the solution and scattering operators for the nonlinear subcritical Klein-Gordon is studied, mainly using these tools and estimates of the nonlinearity in Besov spaces.We prove that these operators are (uniformly) H\uf6lder continuous on the energy space for spacedimension n >= 3, and Lipschitz continuous for