Skip to Main Content

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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Hypoellipticity on Cauchy-Riemann manifolds
HTML articles powered by AMS MathViewer

by Johannes A. Petersen PDF
Trans. Amer. Math. Soc. 334 (1992), 615-639 Request permission


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.
  • R. A. Aĭrapetyan and G. M. Khenkin, Integral representations of differential forms on Cauchy-Riemann manifolds and the theory of CR-functions, Uspekhi Mat. Nauk 39 (1984), no. 3(237), 39–106 (Russian). MR 747791
  • A. Andreotti and C. D. Hill, E. E. Levi convexity and the Hans Lewy problem, Ann. Scuola Norm. Sup. Pisa 26 (1972), 325-363 and 747-806.
  • G. B. Folland and E. M. Stein, Estimates for the $\bar \partial _{b}$ complex and analysis on the Heisenberg group, Comm. Pure Appl. Math. 27 (1974), 429–522. MR 367477, DOI 10.1002/cpa.3160270403
  • G. M. Henkin, H. Lewy’s equation and analysis on pseudoconvex manifolds, Uspehi Mat. Nauk 32 (1977), no. 3(195), 57–118, 247 (Russian). MR 0454067
  • L. Hörmander, Pseudodifferential operators and non-elliptic boundary problems, Ann. of Math. (2) 83 (1966), 129-209.
  • Lars Hörmander, The analysis of linear partial differential operators. I, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 256, Springer-Verlag, Berlin, 1983. Distribution theory and Fourier analysis. MR 717035, DOI 10.1007/978-3-642-96750-4
  • J. J. Kohn and L. Nirenberg, A pseudo-convex domain not admitting a holomorphic support function, Math. Ann. 201 (1973), 265–268. MR 330513, DOI 10.1007/BF01428194
  • H.-M. Maire, Necessary and sufficient condition for maximal hypoellipticity of $\overline \partial _b$, Partial differential equations (Rio de Janeiro, 1986) Lecture Notes in Math., vol. 1324, Springer, Berlin, 1988, pp. 178–185. MR 965534, DOI 10.1007/BFb0100791
  • Alexander Nagel and Jean-Pierre Rosay, Nonexistence of homotopy formula for $(0,1)$ forms on hypersurfaces in $\textbf {C}^3$, Duke Math. J. 58 (1989), no. 3, 823–827. MR 1016447, DOI 10.1215/S0012-7094-89-05838-9
  • Jl. A. Petersen, On the hypoellipticity of the tangential Cauchy-Riemann operator, Thesis, Rutgers Univ., May 1990.
  • François Trèves, Introduction to pseudodifferential and Fourier integral operators. Vol. 2, University Series in Mathematics, Plenum Press, New York-London, 1980. Fourier integral operators. MR 597145
  • François Trèves, Hypoanalytic structures, Microlocal analysis (Boulder, Colo., 1983) Contemp. Math., vol. 27, Amer. Math. Soc., Providence, RI, 1984, pp. 23–44. MR 741037, DOI 10.1090/conm/027/741037
  • François Trèves, Homotopy formulas in the tangential Cauchy-Riemann complex, Mem. Amer. Math. Soc. 87 (1990), no. 434, viii+121. MR 1028234, DOI 10.1090/memo/0434
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 32F20, 32F40, 35H05
  • Retrieve articles in all journals with MSC: 32F20, 32F40, 35H05
Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 334 (1992), 615-639
  • MSC: Primary 32F20; Secondary 32F40, 35H05
  • DOI:
  • MathSciNet review: 1113696