A generalization of Borelʹs theorem and microlocal Gevrey regularity in involutive structures

In this paper, we use Borelʹs procedure to construct Gevrey approximate solutions of an initial value problem for involutive systems of Gevrey complex vector fields. As an application, we describe the Gevrey wave-front set of the boundary values of approximate solutions in wedges of Gevrey involutive structures . We prove that the Gevrey wave-front set of the boundary value is contained in the polar of a certain cone contained in where X is a maximally real edge of . We also prove a partial converse.