  We derive the peak luminosity - peak energy (L_iso - E_peak) correlation
using 22 long Gamma-Ray Bursts (GRBs) with firm redshift measurements. We find
that its slope is similar to the correlation between the time integrated
isotropic emitted energy E_iso and E_peak (Amati et al. 2002). For the 15 GRBs
in our sample with estimated jet opening angle we compute the collimation
corrected peak luminosity L_gamma, and find that it correlates with E_peak.
This has, however, a scatter larger than the correlation between E_peak and
E_gamma (the time integrated emitted energy, corrected for collimation;
Ghirlanda et al. 2004), which we ascribe to the fact that the opening angle is
estimated through the global energetics. We have then selected a large sample
of 442 GRBs with pseudo--redshifts, derived through the lag-luminosity
relation, to test the existence of the L_iso-E_peak correlation. With this
sample we also explore the possibility of a correlation between time resolved
quantities, namely L_iso,p and the peak energy at the peak of emission
E_peak,p.
