  Building on the hyperboloidal foliation approach of Lefloch and Ma, we extend
Klainerman's physical-space approach to dispersive estimates to recover the
frequency-restricted $L^1$--$L^\infty$ dispersive estimates for Klein-Gordon
equations. The hyperboloidal foliation approach naturally only provide
estimates within a fixed forward light-cone, and is based on an initial data
norm that is not translation invariant. Both of these problems can be handled
with frequency-dependent physical-space truncations. To handle the lack of
scaling symmetry for the Klein-Gordon equation and complete the argument, we
also need to keep track of the effectiveness of our estimates in the vanishing
mass limit.
