Skip to main content

Boundary values for the solutions of the \(\bar \partial\)-equation and application to the Nevanlinna class

  • Conference paper
  • First Online:
Spaces of Analytic Functions

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 512))

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. L. Carleson: The Corona theorem. (Proceedings of the 15th Scandinavian Congress, Oslo 1968), Lecture Notes in Mathematics, 118, Springer, Berlin-Heidelberg-New-York, 1970, 121–132.

    MATH  Google Scholar 

  2. G.B. Folland and J.J. Kohn: The Neumann Problem for the Cauchy-Riemann complex. Annals of Mathematic Studies, 75, Princeton University Press, 1972.

    Google Scholar 

  3. G.B. Folland and E.M. Stein: Estimates for the \(\bar \partial _b\)-complex and Analysis on the Heisenberg group. Communication on Pure and Applied Mathematics, 27, 1974, 429–522.

    Article  MathSciNet  MATH  Google Scholar 

  4. L. Gruman: The zeros of holomorphic functions in strictly pseudoconvex domains (to appear in Trans. Amer. Math Soc.)

    Google Scholar 

  5. G.M. Henkin: Integral representations of functions in strictly pseudoconvex domains and application to the \(\bar \partial\)-problem. (In Russian) Math. Sb. 82, 124, 1970, 300–308.

    MathSciNet  Google Scholar 

  6. G.M. Henkin: Preprint, to appear in Doklady Ak. Nauk U.S.S.R., 1975.

    Google Scholar 

  7. L. Hörmander: Generators for some rings of analytic functions. Bull. Amer. Math. Soc. 73, 1967, 943.

    Article  MathSciNet  MATH  Google Scholar 

  8. L. Hörmander: LP estimates for plurisubharmonic functions. Math. Scand. 20, 1967, 65–78.

    MathSciNet  MATH  Google Scholar 

  9. N: Kerzman: Hölder and Lp estimates for the solution of \(\bar \partial u = f\) in strongly pseudoconvex domains. Comm. Pure and Appl. Math. 24, 1971.

    Google Scholar 

  10. G. Laville: Résolution du \(\partial \bar \partial\) avec croissance dans les ouverts pseudoconvexes étoilés de ℂn. C.R. Acad. Sc. Paris, 274, 1972, A–554–556.

    MathSciNet  MATH  Google Scholar 

  11. G. Laville: Diviseurs et classe de Nevanlinna. Thèse de 3è cycle, Université de Paris VI, Juin 1975.

    Google Scholar 

  12. P. Lelong: Fonctionelles analytiques et fonctions entières (n variables). Montrèal, les Presses de l’Université de Montrèal, 1968 (Séminaire de Mathematiques Superieures, été 1967, no 28).

    MATH  Google Scholar 

  13. P. Lelong: Fonctions plurisousharmoniques et formes differentielles positives. Paris-London-New-York, Gordon and Breah, Dunod, 1968.

    MATH  Google Scholar 

  14. I. Lieb: Das Ramirezsche Integral und die Lösung der Gleichung ∂f=α im Bereich der beschränkten Formen. William Marsh Rice University Houston, Texas 56, no 2, Spring 1970.

    Google Scholar 

    Google Scholar 

  15. P. Malliavin, Fonctions de Green d’un ouvert strictement pseudoconvexe et classe de Nevanlinna. C.R. Acad. Sc. Paris, 278, 1974, A–141–144.

    MathSciNet  MATH  Google Scholar 

  16. N. Øvrelid: Integral representation formulas for differential forms and solutions of the \(\bar \partial\)-equation. Colloque international du C.N.R.S. no 208: Fonctions analytiques de plusieures variables et analyse complexe. Agora Mathematica, Paris, Gauthier-Villars, 1974.

    MATH  Google Scholar 

  17. H. Skoda: Valeurs au bord pour les solutions de l’opérateur d″ dans les ouverts strictement pseudoconvexes. C.R. Acad. Sc. Paris, 280, 1975, A–633–636.

    MathSciNet  MATH  Google Scholar 

  18. H. Skoda: Zéros des fonctions de la classe de Nevanlinna dans les ouverts strictment pseudoconvexes. C.R. Acad. Sc. Paris, 280, (23 Juin 1975), A–1677–1680.

    MATH  Google Scholar 

  19. H. Skoda: Valeurs au bord pour les solutions de l’opérateur d″ et caracterisation des zeros des fonctions de la classe de Nevanlinna. Preprint, Centre Universitaire de Toulon et du Var.

    Google Scholar 

Download references

Authors

Editor information

Otto B. Bekken Bernt K. Øksendal Arne Stray

Rights and permissions

Reprints and permissions

Copyright information

© 1976 Springer-Verlag

About this paper

Cite this paper

Skoda, H. (1976). Boundary values for the solutions of the \(\bar \partial\)-equation and application to the Nevanlinna class. In: Bekken, O.B., Øksendal, B.K., Stray, A. (eds) Spaces of Analytic Functions. Lecture Notes in Mathematics, vol 512. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0080032

Download citation

  • DOI: https://doi.org/10.1007/BFb0080032

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07682-7

  • Online ISBN: 978-3-540-38201-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics