The vibrational modes of inertial polarization in the multilayer wire-
like and dot-like structures are determined. The bulk confinement mode
s and the interface ones are separated exactly by a unitary transforma
tion, various additional boundary conditions for the inertial polariza
tion vector being taken into account. The Hamiltonian of the electron-
phonon interaction is deduced. The polaron ground state energy as well
as the effective mass in the cylindrical quantum wire and polaronic s
hift of electron energy levels in the spherical quantum dot are calcul
ated.