Propagation of singularities for operators with constant coefficient hyperbolic-elliptic principal part

Summary In this paper we consider partial differential operators of the type P(x, D)= P_m(D)+Q(x, D), where the constant coefficient principal part P_m is supposed to be hyperbolic-elliptic. We study the propagation of Gevrey singularities for solutions u of the equation P(x, D) u=f, for ultradistributions f, finding exactly to which spaces of ultradistribuiions u microlocally belongs. The results are obtained by constructing a fundamental solution for P when the lower order part Q is with constant coefficients, and a parametrix otherwise.