We investigate the current-voltage characteristics of a p-doped resonant tunneling diode. In the voltage range slightly above the bias corresponding to resonant tunneling of holes into the first light-hole subband of the quantum well, we observe two satellite peaks which we attribute to plasmon-assisted tunneling transitions. A theoretical model is presented to account for these peaks. The model is based on the excitation of intrasubband and intersubband heavy-hole plasmons in the quantum well by hot holes injected close to the energy of the first light-hole subband. We also study the behavior of the satellites when a magnetic field is applied either parallel to or perpendicular to the current.