  In this paper we complete the first step, namely the uniform bound on
completely convergent contributions, towards proving that a three dimensional
interacting system of Fermions is a Fermi liquid in the sense of Salmhofer. The
analysis relies on a direct space decomposition of the propagator, on a bosonic
multiscale cluster expansion and on the Hadamard inequality, rather than on a
Fermionic expansion and an angular analysis in momentum space, as was used in
the recent proof by two of us of Salmhofer's criterion in two dimensions.
