Abstract
Using a recent homotopy formula by Trèves, it is shown that the existence of ( q + 1 ) (q + 1) -dimensional holomorphic supporting manifolds is a sufficient condition for the hypoellipticity on level q q and n − q n - q of a tangential Cauchy-Riemann complex of CR {\text {CR}} -dimension n n . In the hypersurface case, this result is given microlocally.
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