Regularity at the boundary and tangential regularity of solutions of the Cauchy-Riemann system
For a pseudoconvex domain DcCn. we prove the equivalence of the local hypoellipticity of the system (a,a*) with the system (a,ab*) induced at the boundary.
This develops a former result of ours in which the theory of harmonic extension by Kohn was used. This technique is inadequate for the purpose of the present paper and must be replaced by that of the holomorphic extension.