Effect of strong correlation on the electron-phonon interaction

High-T-c superconductors are usually described as strongly correlated elect ronic systems. This feature deeply affects the one-particle and two-particl e properties of the system. In particular, a large incoherent background de velopes on the top of a narrow quasi-particle peak in the one-electron spec tral function. We schematize this structure with a simple phenomenological form. The corresponding Green's function is employed to calculate the charg e response of the system taking into account in a proper way strong correla tion effects. The effective charge interaction acquires a structure in the exchanged momentum space with a predominance of forward scattering, in agre ement with previous numerical calculations. The consequences of the momentu m dependence of the interaction are discussed in the framework of the nonad iabatic theory of superconductivity proposed for the high-T-c materials.