Skip to main content
SpringerLink
Log in

Sobolev estimates for the\(\bar \partial \)-Neumann operator on domains inC n admitting a defining function that is plurisubharmonic on the boundary-Neumann operator on domains inC n admitting a defining function that is plurisubharmonic on the boundary

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Barrett, D.E.: Regularity of the Bergman projection on domains with transverse symmetries. Math. Ann.258, 441–446 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  2. Barrett, D.E.: Regularity of the Bergman projection and local geometry of domains. Duke Math. J.53, 333–343 (1986)

    MATH  MathSciNet  Google Scholar 

  3. Bedford, E.: Proper holomorphic mappings. Bull. Am. Math. Soc.10, 157–175 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  4. Bell, S.R.: Biholomorphic mappings and the\(\bar \partial \)-Neumann problem. Ann. Math.114, 103–113 (1981)

    Article  Google Scholar 

  5. Bell, S.R.: Boundary behavior of proper holomorphic mappings between non-pseudoconvex domains. Am. J. Math.106, 639–643 (1984)

    Article  MATH  Google Scholar 

  6. Bell, S., Catlin, D.: Boundary regularity of proper holomorphic mappings. Duke Math. J.49, 385–396 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  7. Boas, H.P., Chen, S.C., Straube, E.J.: Exact regularity of the Bergman and Szegö projections on domains with partially transverse symmetries. Manuscr. Math.62, 467–475 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  8. Boas, H.P., Shaw, M.C.: Sobolev estimates for the Lewy operator on weakly pseudo-convex boundaries. Math. Ann.274, 221–231 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  9. Boas, H.P., Straube, E.J.: Complete Hartogs domains inC 2 have regular Bergman and Szegö projections. Math. Z.201, 441–454 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  10. Boas, H.P., Straube, E.J.: Equivalence of regularity for the Bergman projection and the\(\bar \partial \)-Neumann operator, Manuscr. Math.67, 25–33 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  11. Boas, H.P., Straube, E.J.: The Bergman projection on Hartogs domains in C2. Trans. Am. Math. Soc., (to appear)

  12. Bonami, A., Charpentier, P.: Une estimation Sobolev 1/2 pour le projecteur de Bergman. C. R. Acad. Sci. Paris307, 173–176 (1988)

    MATH  MathSciNet  Google Scholar 

  13. Bonami, A., Charpentier, P.: Boundary values for the canonical solution to\(\bar \partial \)-equation andW 1/2 estimates. (preprint)

  14. Chen, S.-C.: Global analytic hypoellipticity of the\(\bar \partial \)-Neumann problem on circular domains. Invent. Math.92, 173–185 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  15. Chen, S.-C.: Global regularity of the\(\bar \partial \)-Neumann problem on circular domains. Math. Ann.285, 1–12 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  16. Chen, S.-C.: Global regularity of the\(\bar \partial \)-Neumann problem: a sufficient condition. (preprint)

  17. Chen. S.-C.: Global regularity of the\(\bar \partial \)-Neumann problem in dimension two. (preprint)

  18. Derridj, M.: Regularité pour\(\bar \partial \) dans quelques domaines faiblement pseudoconvexes. J. Differ. Geom.13, 559–576 (1978)

    MATH  MathSciNet  Google Scholar 

  19. Derridj, M., Tartakoff, D.S.: On the global real analyticity of solutions to the\(\bar \partial \)-Neumann problem. Commun. Partial Differ. Equations1, 401–435 (1976)

    MATH  MathSciNet  Google Scholar 

  20. Diederich, K., Fornæss J.E.: Pseudoconvex domains: an example with nontrivial Nebenhülle. Math. Ann.225, 275–292 (1978)

    Article  Google Scholar 

  21. Diederich, K., Fornæss, J.E.: Boundary regularity of proper holomorphic mappings. Invent. Math.67, 363–384 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  22. Folland, G.B., Kohn, J.J.: The Neumann Problem for the Cauchy-Riemann Complex Ann. Math. Stud. Vol. 75, Princeton: Princeton Univ. Press 1972

    MATH  Google Scholar 

  23. Forstnerič, F.: Proper holomorphic mappings: a survey. In: J.E. Fornaess (ed.) Several Complex Variables. Proc. Mittag-Leffler Inst. 1987–1988. Princeton: Princeton University Press 1990

    Google Scholar 

  24. Hörmander, L.:L 2 estimates and existence theorems for the\(\bar \partial \) operator. Acta. Math.113, 89–152 (1965)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  26. Kohn, J.J.: A survey of the\(\bar \partial \)-Neumann problem. In: Proc. Symp. Pure Math, vol. 41, Am. Math. Soc., Providence, 1984, pp. 137–145

  27. Kohn, J.J.: The range of the tangential Cauchy-Riemann operator. Duke Math. J.53, 525–545 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  28. Komatsu, G.: Global analytic-hypoellipticity of the\(\bar \partial \)-Neumann problem. Tôhoku Math. J.28, 145–156 (1976)

    MATH  MathSciNet  Google Scholar 

  29. Krantz, S.G.: Function Theory of Several Complex Variables. New York: Wiley 1982

    MATH  Google Scholar 

  30. Noell, A.: Local versus global convexity of pseudoconvex domains. (preprint)

  31. Range, R.M.: Holomorphic Functions and Integral Representations in Several Complex Variables. Berlin Heidelberg New York: Springer 1986

    MATH  Google Scholar 

  32. Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton, N.J. 1970

    MATH  Google Scholar 

  33. Shaw, M.-C.:L 2 estimates and existence theorems for the tangential Cauchy-Riemann complex. Invent. Math.82, 133–150 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  34. Straube, E.J.: Exact regularity of Bergman, Szegö, and Sobolev space projections in non pseudoconvex domains. Math. Z.192, 117–128 (1986)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Harold P. Boas & Emil J. Straube

Authors
  1. Harold P. Boas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Emil J. Straube
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This paper is a revision (May 1990) of our preprint formerly titled “Sobolev estimates for the\(\bar \partial \)-Neumann operator on convex domains inC n”.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Boas, H.P., Straube, E.J. Sobolev estimates for the\(\bar \partial \)-Neumann operator on domains inC n admitting a defining function that is plurisubharmonic on the boundary-Neumann operator on domains inC n admitting a defining function that is plurisubharmonic on the boundary. Math Z 206, 81–88 (1991). https://doi.org/10.1007/BF02571327

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02571327

Keywords

Search

Navigation