Hypoellipticity on Cauchy-Riemann manifolds

Petersen, Johannes A.

doi:10.1090/S0002-9947-1992-1113696-6

Hypoellipticity on Cauchy-Riemann manifolds
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by Johannes A. Petersen

Trans. Amer. Math. Soc. 334 (1992), 615-639

DOI: https://doi.org/10.1090/S0002-9947-1992-1113696-6

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Abstract:

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

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