  The Einstein equations in wave map gauge are a geometric second order system
for a Lorentzian metric. To study existence of solutions of this hyperbolic
quasi diagonal system with initial data on a characteristic cone which are not
zero in a neighbourhood of the vertex one can appeal to theorems due to Cagnac
and Dossa, proved for a scalar wave equation, for initial data in functional
spaces relevant for their proofs. It is difficult to check that the initial
data that we have constructed as solutions of the Einstein wave-map gauge
constraints satisfy the more general of the Cagnac-Dossa hypotheses which uses
weighted energy estimates. In this paper we start a new study of energy
estimates using on the cone coordinates adapted to its null structure which are
precisely the coordinates used to solve the constraints, following work of
Rendall who considered the Cauchy problem for Einstein equations with data on
two intersecting characteristic surfaces.
