Local analytic hypoellipticity for □b on nondegenerate Cauchy—Riemann manifolds

摘要

The local real analytic regularity of solutions to □b, the complex boundary Laplacian, and related operators is proved for (p,q) forms on a nondegenerate, abstract, real analytic Cauchy-Riemann (C-R) manifold of dimension 2n - 1 satisfying J. J. Kohn's condition Y(q). The problem is reduced to the study of general, “variable coefficient” operators, satisfying the same a priori estimates, on the Heisenberg group. L² methods only are used.