  Using the dipole framework for QCD at small x in the 1/N_c limit, we derive
the expression of the 1 -> p dipole multiplicity density in momentum space.
This gives an analytical expression for the 1 -> p QCD Pomeron amplitudes in
terms of one-loop integration of effective vertices in transverse momentum.
Conformal invariance and a Hilbert space construction for dipole correlation
functions are the main tools of the derivation. Relations with conformal field
theories in the classical limit are discussed.
