Local Gevrey and Quasi - Analytic Hypoellipticity For

Introduction. The db complex is well defined on any smooth CR manifold M, and once a metric is fixed, so is the complex Laplace-Beltrami operator Db on forms of type (p, q). For compact M without boundary, the bb cohomology of M may be studied via Ub [6], and thus local smoothness of solutions to Dbu = ƒ is important. In its own right, Ub is a prototype of doubly characteristic operators. Under suitable convexity conditions on M, Kohn [7] established the following subelliptic estimate on (p, q) forms in CQ(M):