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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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The complex Green operator on CR-submanifolds of $\mathbb {C}^{n}$ of hypersurface type: Compactness
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by Emil J. Straube PDF
Trans. Amer. Math. Soc. 364 (2012), 4107-4125 Request permission


We establish compactness estimates for $\overline {\partial }_{b}$ on a compact pseudoconvex CR-submanifold of $\mathbb {C}^{n}$ of hypersurface type that satisfies property(P). When the submanifold is orientable, these estimates were proved by A. Raich in 2010 using microlocal methods. Our proof deduces the estimates from (a slight extension, when $q>1$, of) those known on hypersurfaces via the fact that locally, CR-submanifolds of hypersurface type are CR-equivalent to a hypersurface. The relationship between two potential theoretic conditions is also clarified.
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Additional Information
  • Emil J. Straube
  • Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
  • MR Author ID: 168030
  • Email:
  • Received by editor(s): July 5, 2010
  • Received by editor(s) in revised form: August 9, 2010
  • Published electronically: March 15, 2012
  • Additional Notes: This research was supported in part by NSF grant DMS 0758534
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 364 (2012), 4107-4125
  • MSC (2010): Primary 32W10, 32V99
  • DOI:
  • MathSciNet review: 2912447