  We study the interaction of electrons with phonons in strongly correlated
solids, having high-T_c cuprates in mind. Using sum-rules, we show that the
apparent strength of this interaction strongly depends on the property studied.
If the solid has a small fraction (doping) delta of charge carriers, the
influence of the interaction on the phonon self-energy is reduced by a factor
delta, while there is no corresponding reduction of the coupling seen in the
electron self-energy. This supports the interpretation of recent photoemission
experiments, assuming a strong coupling to phonons.

Strongly Correlated Electrons;Materials Science