Regularity at the Boundary and Tangential Regularity

For a pseudoconvex domain in complex space, we prove the equivalence of the local hypoellipticity of the system (di-bar, di-bar*) with the system (di-bar_b,di-bar*_b) induced in the boundary. This develops a result of ours which used the theory of the “harmonic” extension by Kohn. This technique is inadequate for the purpose of the present paper and must be replaced by the “holomorphic” extension introduced by the authors in former work.