We consider the wave and Klein-Gordon equations on the real hyperbolic space
Hn (n≥2) in a framework based on weak-Lp spaces.
First, we establish dispersive estimates on Lorentz spaces in the context of
Hn. Then, employing those estimates, we prove global
well-posedness of solutions and an exponential asymptotic stability property.
Moreover, we develop a scattering theory in such singular framework.Comment: 15 page