Skip to main content
SpringerLink
Log in

L 2 estimates and existence theorems for the\(\bar \partial \) operator

  • Published:
Acta Mathematica

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. Andreotti, A. &Grauert, H., Théorèmes de finitude pour la cohomologie des espaces complexes.Bull. Soc. Math. France, 90 (1962), 193–259.

    MATH  MathSciNet  Google Scholar 

  2. Ash, M. E., The basic estimate of the\(\bar \partial \)-Neumann problem in the non-Kählerian case.Amer. J. Math., 86 (1964), 247–254.

    Article  MATH  MathSciNet  Google Scholar 

  3. Bergman, S., Über die Kernfunktion eines Bereiches und ihr Verhalten am Rande. I–II.J. Reine Angew. Math., 169 (1933), 1–42, and 172 (1935), 89–128.

    Google Scholar 

  4. Bers, L.,Several complex variables. Lecture notes, New York University, 1963.

  5. Bremermann, H., Complex convexity.Trans. Amer. Math. Soc., 82 (1956), 17–51.

    Article  MATH  MathSciNet  Google Scholar 

  6. —, Über die Äquivalenz der pseudoconvexen Gebiete und der Holomorphiegebiete im Raum vonn komplexen Veränderlichen.Math. Ann., 128 (1954), 63–91.

    Article  MATH  MathSciNet  Google Scholar 

  7. Cartan, H.,Séminaires E.N.S. 1951/1952.

  8. Ehrenpreis, L., Some applications of the theory of distributions to several complex variables.Seminar on analytic functions I, 65–79. Institute for Advanced Study, Princeton 1957.

    Google Scholar 

  9. Ehrenpreis, L., A fundamental principle for systems of linear differential equations with constant coefficients, and some of its applications.Proc. Intern. Symp. on Linear spaces, Jerusalem 1961, 161–174.

  10. Friedrichs, K., The identity of weak and strong extensions of differential operators.Trans. Amer. Math. Soc., 55 (1944), 132–151.

    Article  MATH  MathSciNet  Google Scholar 

  11. Garabedian, P. R. &Spencer, D. C., Complex boundary problems.Trans. Amer. Math. Soc., 73 (1952), 223–242.

    Article  MATH  MathSciNet  Google Scholar 

  12. Hörmander, L.,Linear partial differential operators. Springer 1963.

  13. —, Weak and strong extensions of differential operators.Comm. Pure Appl. Math., 14 (1961), 371–379.

    MATH  MathSciNet  Google Scholar 

  14. Kohn, J. J., Harmonic integrals on strongly pseudo-convex manifolds I.Ann. Math. (2), 78 (1963), 112–148.

    MATH  MathSciNet  Google Scholar 

  15. —, Regularity at the boundary of the\(\bar \partial \)-Neumann problem.Proc. Nat. Acad. Sci. U.S.A., 49 (1963), 206–213.

    Article  MATH  MathSciNet  Google Scholar 

  16. —, Harmonic integrals on strongly pseudo-convex manifolds II.Ann. Math. (2), 79 (1964), 450–472.

    MATH  MathSciNet  Google Scholar 

  17. Lax, P. D. &Phillips, R. S., Local boundary conditions for dissipative symmetric linear differential operators.Comm. Pure Appl. Math. 13 (1960), 427–455.

    MATH  MathSciNet  Google Scholar 

  18. Lelong, P., Les fonctions plurisousharmoniques.Ann. Sci. École Norm. Sup. 62 (1945) 301–338.

    MATH  MathSciNet  Google Scholar 

  19. Malgrange, B.,Lectures on the theory of functions of several complex variables. Tata Institute of Fundamental Research, Bombay 1958.

    MATH  Google Scholar 

  20. Malgrange, B., Sur les systèmes differentiels a coefficients constants.Coll. int. du CNRS, Paris 1963.

  21. Martineau, A., Sur les fonctionnelles analytiques et la transformation de Fourier-Borel.J. Analyse Math., 9 (1963), 1–164.

    Article  MathSciNet  Google Scholar 

  22. Morse, A. P., The behavior of a function on its critical set.Ann. Math. (2), 40 (1939), 62–70.

    MATH  Google Scholar 

  23. Morrey, C. B., The analytic embedding of abstract real analytic manifolds.Ann. Math. (2), 68 (1958), 159–201.

    Article  MATH  MathSciNet  Google Scholar 

  24. Nagy, B. v. Sz.,Spektraldarstellung linearer Transformationen des Hilbertschen Raumes. Berlin 1942.

  25. Newlander, A. &Nirenberg, L., Complex analytic coordinates in almost complex manifolds.Ann. Math. (2), 65 (1957), 391–404.

    MATH  MathSciNet  Google Scholar 

  26. Norguet, F., Sur les domaines d'holomorphie des fonctions uniformes de plusieurs variables complexes.Bull. Soc. Math. France, 82 (1954), 137–159.

    MATH  MathSciNet  Google Scholar 

  27. Oka, K., Sur les fonctions analytiques de plusieurs variables. VI. Domaines pseudoconvexes.Tôhuku Math. J., 49 (1942), 19–52.

    MathSciNet  Google Scholar 

  28. —, Sur les fonctions analytiques de plusieurs variables. IX. Domaines finis sans point critique interieur.Japan J. Math., 23 (1954), 97–155.

    MathSciNet  Google Scholar 

  29. Pólya, G., Untersuchungen über Lücken und Singularitäten von Potenzreihen.Math. Z., 29 (1929), 549–640.

    Article  MATH  MathSciNet  Google Scholar 

  30. Weil, A.,Variétés Kählériennes. Hermann, Paris, 1958.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The Institute for Advanced Study, Princeton, N. J., USA

    Lars Hörmander

Authors
  1. Lars Hörmander
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This investigation was supported by the Office of Naval Research under contract No. 225(11) at Stanford University.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hörmander, L. L 2 estimates and existence theorems for the\(\bar \partial \) operator. Acta Math. 113, 89–152 (1965). https://doi.org/10.1007/BF02391775

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02391775

Keywords

Search

Navigation