  We develop a unified treatment of the piesoelectric coupling between
two-dimensional electrons and bulk phonons in both cases of zero and strong
magnetic fields, the latter corresponding to even denominator filling
fractions. In contrast to the case of coupling via the deformation potential,
the leading contributions due to impurity-renormalized electron-phonon vertices
are not exactly cancelled by processes of inelastic electron-impurity
scattering. Electron energy relaxation time, diffusion correction to the
conductivity, and phonon emission rate by hot electrons are computed for
realistic $GaAs/AlGaAs$ heterostructures.
