On the decay and scattering for the Klein-Gordon-Hartree equation with radial data

In this paper, we study the decay estimate and scattering theory for the Klein-Gordon-Hartree equation with radial data in space dimension d ≥ 3. By means of a compactness strategy and two Morawetz-type estimates which come from the linear and nonlinear parts of the equation, respectively, we obtain the corresponding theory for energy subcritical and critical cases. The exponent range of the decay estimates is extended to 0 < γ ≤ 4 and γ < d with Hartree potential V (x) = |x| ^-γ.