  The Regge limit in perturbative QCD for processes as DIS (low x) and photon
or onia-particles scattering is considered. In the first part a
phenomenological approach for the inclusion of the running coupling, preserving
the gluon reggeization property, is analyzed. In particular the spectrum of the
hard pomeron equation and the asymptotic form of the solution are used to study
scattering processes with also inclusive jet production. The singlet part of
the proton structure function is evolved towards the low x region according to
the full equation. In the second part the problem of unitarity in the QCD is
considered. Following the general Bartels approach the four reggeized gluon
system is studied in the large number of colours limit. The interplay between
double pomeron exchange and triple pomeron vertex contributions is studied. The
conformal invariance of the three pomeron vertex is shown in terms of a
building block function, and the coupling to pomerons has been considered to
make contact with the colour dipole picture which presents a similar triple
pomeron interaction. It is also shown that in the A.H. Mueller approach his
equation for higher order colour dipole densities leads to solutions which can
be represented as fan diagrams with only triple pomeron vertices. Finally we
draw some conclusion and open problems.
