For a pseudoconvex domain
D ⊂ ℂn, we prove the equivalence of the local hypoellipticity of the system (∂,∂∗)
with the system (∂b,∂b∗) 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.