Skip to main content
Log in

Behavior of the Bergman projection on the Diederich-Fornæss worm

  • Published:
Acta Mathematica

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  • [Ba1]Barrett, D., Irregularity of the Bergman projection on a smooth bounded domain in C2.Ann. of Math., 119 (1984), 431–436.

    Article  MATH  MathSciNet  Google Scholar 

  • [Ba2]—, Biholomorphic domains with inequivalent boundaries.Invent. Math., 86 (1986). 373–377.

    Article  MathSciNet  Google Scholar 

  • [BF]Barrett, D. &Forness, J. E., Uniform approximation of holomorphic functions on bounded Hartogs domains in C2.Math. Z., 191 (1986), 61–72.

    Article  MATH  MathSciNet  Google Scholar 

  • [Be]Bell, S., Biholomorphic mappings and the\(\bar \partial \)-problem.Ann. of Math., 114 (1981), 103–113.

    Article  MATH  MathSciNet  Google Scholar 

  • [BL]Bell, S. &Ligocka, E., A simplication and extension of Fefferman’s theorems on biholomorphic mappings.Invet. Math., 57 (1980), 2383–289.

    MathSciNet  Google Scholar 

  • [BSt1]Boas, H. & Straube, E., Sobolev estimates for the\(\bar \partial \)-Neumann operator on domains in Cn admitting a defining function that is plurisubharmonic on the boundary. Preprint.

  • [BSt2]— Equivalence of regularity for the Bergman projection and the\(\bar \partial \)-Neumann operator.Manuscripta Math., 67 (1990) 25–33.

    MATH  MathSciNet  Google Scholar 

  • [BSt3]Boas, H., The Bergman projection on Hartogs domains in C2. Preprint.

  • [Ca]Catlin, D., Global regularity of the\(\bar \partial \)-Neumann problem.Proc. Sympos. Pure Math., 41 (1984), 39–49.

    MATH  MathSciNet  Google Scholar 

  • [Ch]Chen, So-Chin, Global regularity of the\(\bar \partial \)-Neumann problem in dimension two. Preprint.

  • [DF]Diederich, K. &Fornaess, J. E., Pseudoconvex domains: an example with nontrivial Nebenhulle.Math. Ann., 225 (1977), 275–292.

    Article  MATH  MathSciNet  Google Scholar 

  • [FK]Folland, G. & Kohn, J. J.,The Neumann Problem for the Cauchy-Riemann Complex. Ann of Math. Studies, no. 75. Princeton Univ. Press, 1972.

  • [Ki]Kiselman, C., A study of the Bergman projection in certain Hartogs domains. Preprint.

  • [Ko1]Kohn, J. J., Global regularity for\(\bar \partial \) on weakly pseudoconvex manifolds.Trans. Amer. Math. Soc., 181 (1973), 273–292.

    Article  MATH  MathSciNet  Google Scholar 

  • [Ko2]—, Subellipticity of the\(\bar \partial \)-Neumann problem on pseudoconvex domains: sufficient conditions.Acta Math., 142 (1979), 79–122.

    Article  MATH  MathSciNet  Google Scholar 

  • [Li]Ligocka, E., Estimates in Sobolev norms ∥·∥ s p for harmonic and holomorphic functions and interpolation between Sobolev and Hölder spaces of harmonic functions.Studia Math., 86 (1987), 255–271.

    MATH  MathSciNet  Google Scholar 

  • [Si]Sibony, N., Une classe de domaines pseudoconvexes.Duke Math. J., 55 (1987), 299–319.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Barrett, D.E. Behavior of the Bergman projection on the Diederich-Fornæss worm. Acta Math 168, 1–10 (1992). https://doi.org/10.1007/BF02392975

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02392975

Keywords

Navigation