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We show that the knowledge of the Dirichlet-to-Neumann map on the boundary ofa bounded open set in $R^n$ for the perturbed polyharmonic operator$(-\Delta)^m +q$ with $q\in L^{n/2m}$, $n>2m$, determines the potential $q$ inthe set uniquely. In the course of the proof, we construct a special Greenfunction for the polyharmonic operator and establish its mapping properties insuitable weighted $L^2$ and $L^p$ spaces. The $L^p$ estimates for the specialGreen function are derived from $L^p$ Carleman estimates with linear weightsfor the polyharmonic operator.

Inverse boundary problems for polyharmonic operators with unbounded potentials