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Local analytic hypoellipticity for square(b) on nondegenerate Cauchy-Riemann manifolds.

The local real analytic regularity of solutions to square(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. L(2) methods only are used.