  After describing the inhomogeneous equation suitable to describe
W{\nu}{\mu}{\rho}{\sigma}, a solution of the linearized version of the full
quasilinear equation for the conformal part of the Riemann tensor connected to
the perturbations of the Kerr spacetime far from the origin, we find the right
decays we have to impose to the source term to obtain the peeling decays for
this linearized solution. We basically follow the ideas of the Christodoulou
Klainerman approach, [Ch-Kl] and [Kl-Ni1]. This result requires some new
detailed estimates which could be considered a useful result by themselves.
