C^(inf)-regularity of solutions of the tangential CR-equations on weakly pseudoconvex manifolds

Math. Ann. 311, 147–162 (1998)

Mathematische Annalen c Springer-Verlag 1998

C ∞ -regularity of solutions of the tangential CR-equations on weakly pseudoconvex manifolds Joachim Michel1 , Mei-Chi Shaw2, ? 1 Universit´ e Du Littoral, Centre Universitaire de la Mi-Voix, F-62228 Calais, France (e-mail: [email protected]) 2 Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556, USA (e-mail: [email protected])

Received: 3 August 1997 / Accepted: 17 September 1997

Mathematics Subject Classification (1991): 32F30, 35N10, 32F20 Let Ω be a bounded weakly pseudoconvex domain in Cn with C ∞ boundary bΩ. The existence of C ∞ solutions up to the boundary for the ∂-equation was shown by J. J. Kohn [6]. In the present paper we give an analogous result for the tangential Cauchy-Riemann equations on compact 2n − 1-dimensional submanifolds M in bΩ with boundary. Here the boundary of M is defined by the transversal intersection of bΩ and a hypersurface H = {z |