  The lattice dynamics of Ba$_2$CuGe$_2$O$_7$, a compound which develops
Dzyaloshinsky-Moriya (DM) helical magnetism below $T_N$ = 3.2 K, has been
studied by measuring the infrared reflectivity of a single crystal with the
radiation polarized both in the $ab$ plane and along the $c$ axis of its
tetragonal cell, from 7 K to 300 K. In this compound, where the unit cell has
no inversion symmetry, fourteen $E$ phonon modes of the $ab$ plane, out of the
eighteen predicted, and all the ten $B_2$ modes of the $c$ axis, have been
observed. They have been assigned to the atomic motions by a comparison with
shell-model calculations, which provided vibrational frequencies in good
agreement with the experiment, while most calculated intensities turned to be
much lower than the experimental values. This discrepancy has been tentatively
explained by assuming strong electron-phonon interactions, a hypothesis
supported by the failure of the $f$- sum rule if restricted to the phonon
region. Indeed, we observe a remarkable increase in the oscillator strengths at
$T$'s low but higher than $T_N$, which suggests that the dielectric constant of
Ba$_2$CuGe$_2$O$_7$ may increase at those temperatures.
