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Equivalence of regularity for the Bergman projection and the\(\bar \partial\)-neumann operator

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Abstract

A necessary and sufficient condition for regularity of the\(\bar \partial\)-Neumann operator on (0,q)-forms in a smooth bounded pseudoconvex domain in Cn is that the orthogonal projections onto\(\bar \partial\)-closed forms of degrees (0,q−1), (0,q), and (0,q+1) all be regular.

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References

  1. Steve Bell and David Catlin,Boundary regularity of proper holomorphic mappings, Duke Math. J.49 (1982), 385–396

    Article  MATH  MathSciNet  Google Scholar 

  2. Harold P. Boas, So-Chin Chen, and Emil J. Straube,Exact regularity of the Bergman and Szegö projections on domains with partially transverse symmetries, manuscripta math.62 (1988), 467–475

    Article  MATH  MathSciNet  Google Scholar 

  3. Harold P. Boas, Small sets of infinite type are benign for the\(\bar \partial\)-Neumann problem, Proc. Amer. Math. Soc.103 (1988), 569–578

    Article  MATH  MathSciNet  Google Scholar 

  4. Klas Diederich and John Erik Fornæss,Boundary regularity of proper holomorphic mappings, Invent. Math.67 (1982), 363–384

    Article  MATH  MathSciNet  Google Scholar 

  5. G. B. Folland and J. J. Kohn, “The Neumann problem for the Cauchy-Riemann complex” Princeton Univ. Press, Princeton, 1972

    MATH  Google Scholar 

  6. J. J. Kohn, Global regularity for\(\bar \partial\) on weakly pseudo-convex manifolds, Trans. Amer. Math. Soc.181 (1973), 273–292

    Article  MATH  MathSciNet  Google Scholar 

  7. J. J. Kohn, A survey of the\(\bar \partial\)-Neumann problem, in “Proc. Symp. Pure Math., vol. 41,” Amer. Math. Soc., Providence, 1984, pp. 137–145

    Google Scholar 

  8. Steven G. Krantz, Compactness of the\(\bar \partial\)-Neumann operator, Proc. Amer. Math. Soc.103 (1988), 1136–1138

    Article  MATH  MathSciNet  Google Scholar 

  9. Ewa Ligocka,The regularity of the weighted Bergman projections, in “Lecture Notes in Math., vol. 1165” Springer, New York, 1985, pp. 197–203

    Google Scholar 

  10. R. Michael Range,The \(\bar \partial\)-Neumann operator on the unit ball in C n, Math. Ann.266 (1984), 449–456

    Article  MATH  MathSciNet  Google Scholar 

  11. Norberto Salinas, Albert Sheu, and Harald Upmeier,Toeplitz operators on pseudoconvex domains and foliation C *-algebras, Annals of Math.130 (1989), 531–565

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Texas A&M University, 77843, College Station, TX, USA

    Harold P. Boas & Emil J. Straube

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  1. Harold P. Boas
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  2. Emil J. Straube
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The first author partially supported by NSF Grant DMS-8701038

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Boas, H.P., Straube, E.J. Equivalence of regularity for the Bergman projection and the\(\bar \partial\)-neumann operator. Manuscripta Math 67, 25–33 (1990). https://doi.org/10.1007/BF02568420

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  • DOI: https://doi.org/10.1007/BF02568420

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