  A proof is given that the space $\L$ of solutions of the linearized vacuum
Einstein's equation around a Schwarzschild black hole is parameterized by two
scalar fields which are gauge invariant combinations of perturbed algebraic and
differential invariants of the Weyl tensor, and encode the information on the
odd (-) and even (+) sectors $\L_{\pm}$ These fields measure the distortion of
the geometry caused by a generic perturbation, and are shown to be pointwise
bounded on the outer region $r \geq 2M$.
