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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Compactness of the $\overline \partial$-Neumann operator
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by Steven G. Krantz PDF
Proc. Amer. Math. Soc. 103 (1988), 1136-1138 Request permission

Abstract:

This paper gives an elementary construction of smooth, bounded pseudoconvex domains which satisfy Condition $R$ but which do not have compact $\bar \partial$-Neumann operator.
References
  • Steven R. Bell, Biholomorphic mappings and the $\bar \partial$-problem, Ann. of Math. (2) 114 (1981), no. 1, 103–113. MR 625347, DOI 10.2307/1971379
  • Steven R. Bell and Harold P. Boas, Regularity of the Bergman projection in weakly pseudoconvex domains, Math. Ann. 257 (1981), no. 1, 23–30. MR 630644, DOI 10.1007/BF01450652
  • H. P. Boas, Small sets of infinite type are benign for the $\bar \partial$-Neumann problem, preprint. D. Catlin, Subelliptic estimates for the $\bar \partial$-Neumann problem on pseudoconvex domains, Ann. of Math. (in press). —, Global regularity of the $\bar \partial$-Neumann problem, Proc. Sympos. Pure Math., vol. 41, Amer. Math. Soc., Providence, R. I., 1984.
  • G. B. Folland and J. J. Kohn, The Neumann problem for the Cauchy-Riemann complex, Annals of Mathematics Studies, No. 75, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1972. MR 0461588
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Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 103 (1988), 1136-1138
  • MSC: Primary 32F20; Secondary 32A07, 35N15
  • DOI: https://doi.org/10.1090/S0002-9939-1988-0954995-2
  • MathSciNet review: 954995