A remark concerning the theory of scattering for a perturbed polyharmonic operator

Let $R_0$ and $R$ be resolvents of the operators $(-\Delta)^l$ and $(-\Delta)^l+q$ acting in $L_2(E^m)$. We study the problem of the belonging of the operator $R^P-R_0^p$ to various symmetrically-normed ideals of the ring of bounded operators. We give applications to the theory of scattering.