  We show that the knowledge of the Dirichlet-to-Neumann map on the boundary of
a bounded open set in $\mathbb R^n$, $n\ge 3$, for the perturbed polyharmonic
operator $(-\Delta)^m+A\cdot D+q$, $m\ge 2$, with $n>m$, $A\in
W^{-\frac{m-2}{2},\frac{2n}{m}}$ and $q\in
W^{-\frac{m}{2}+\delta,\frac{2n}{m}}$, with $0<\delta<1/2$, determines the
potentials $A$ and $q$ in the set uniquely. The proof is based on a Carleman
estimate with linear weights and with a gain of two derivatives and on the
property of products of functions in Sobolev spaces.
