Isolated photon + jet photoproduction as a tool to constrain the gluon distribution in the proton and the photon

We analyse how the reaction gamma p -> gamma + jet + X can serve to constrain the gluon distributions. Our results are based on a code of partonic event generator type which includes full NLO corrections. We conclude that there are phase space domains in which either the gluon in the photon or the gluon in the proton give important contributions to the cross section, which should be observable in HERA experiments.