  We study effects of the Coulomb repulsion on the electron-phonon interaction
(EPI) in a model of cuprates at zero and finite doping. We find that
antiferromagnetic correlations strongly enhance EPI effects on the electron
Green's function with respect to the paramagnetic correlated system, but the
net effect of the Coulomb interaction is a moderate suppression of the EPI.
Doping leads to additional suppression, due to reduced antiferromagnetic
correlations. In contrast, the Coulomb interaction strongly suppresses EPI
effects on phonons, but the suppression weakens with doping.
