Skip to main content
SpringerLink
Log in

Uniqueness Properties of Hardy Space Functions

  • Published:
The Journal of Geometric Analysis Aims and scope Submit manuscript

Abstract

We study the boundary uniqueness properties of Hardy space functions in several complex variables. Along the way, we develop properties of the Lumer Hardy space.

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

Similar content being viewed by others

Notes

  1. See [3] for the provenance of the Painelvé result.

References

  1. Bagemihl, F., Seidel, W.: Some boundary properties of analytic functions. Math. Z. 61, 186–199 (1954)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bell, S.R., Krantz, S.G.: Smoothness to the boundary of conformal mappings. Rocky Mt. J. Math. 17, 23–40 (1987)

    Article  MATH  Google Scholar 

  3. Burckel, R.: An Introduction to Classical Complex Analysis. Vol. 1: Pure and Applied Mathematics, vol. 82. Academic Press, Inc., New York (1979)

    Book  MATH  Google Scholar 

  4. Cima, J.A., Krantz, S.G.: A Lindelöf principle and normal functions in several complex variables. Duke Math. J. 50, 303–328 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  5. Collingwood, E.F., Lohwater, A.J.: The Theory of Cluster Sets. Cambridge University Press, Cambridge (1966)

    Book  MATH  Google Scholar 

  6. Duren, P.: The Theory of \(H^p\) Spaces. Academic Press, New York (1970)

    MATH  Google Scholar 

  7. Fefferman, C.: The Bergman kernel and biholomorphic mappings of pseudoconvex domains. Invent. Math. 26, 1–65 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  8. Greene, R.E., Krantz, S.G.: Function Theory of One Complex Variable, 3rd edn. American Mathematical Society, Providence (2006)

    MATH  Google Scholar 

  9. Hakim, M., Sibony, N.: Boundary properties of holomorphic functions in the ball of \(\mathbb{C}^n\). Math. Ann. 276, 549–555 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  10. Hirsch, M.: Differential Topology. Springer, New York (1976)

    Book  MATH  Google Scholar 

  11. Krantz, S.G.: Partial Differential Equations and Complex Analysis. CRC Press, Boca Raton (1992)

    MATH  Google Scholar 

  12. Krantz, S.G.: Function Theory of Several Complex Variables, 2nd edn. American Mathematical Society, Providence (2001)

    MATH  Google Scholar 

  13. Krantz, S.G.: The Lindelöf principle in several complex variables. J. Math. Anal. Appl. 326, 1190–1198 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  14. Lehto, O., Virtanen, K.: Boundary behavior and normal meromorphic functions. Acta Math. 97, 47–65 (1957)

    Article  MathSciNet  MATH  Google Scholar 

  15. Lempert, L.: Boundary behavoiur of meromorphic functions of several variables. Acta Math. 144, 1–25 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  16. Lumer, G.: Espaces de Hardy en plusiers variables complexes. C. R. Acad. Sci. Paris Sér. A–B 273, 151–154 (1971)

    MATH  Google Scholar 

  17. Nagel, A., Rudin, W.: Local boundary behavior of bounded holomorphic functions. Can. J. Math. 30, 583–592 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  18. Pommerenke, C.: Boundary Behaviour of Conformal Maps, Grundlehren der Mathematischen Wissenschaften, 299. Springer, Berlin (1992)

    Book  Google Scholar 

  19. Rudin, W.: Lumer’s Hardy spaces. Mich. J. Math. 24, 1–5 (1977)

    Article  MathSciNet  Google Scholar 

  20. Stein, E.M.: Singular Integrals and Differentiability Properties of Functions. Princeton University Press, Princeton (1970)

    MATH  Google Scholar 

  21. Stein, E.M.: Boundary Behavior of Holomorphic Functions of Several Complex Variables. Princeton University Press, Princeton (1972)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Washington University in St. Louis, St. Louis, MO, 63130, USA

    Steven G. Krantz

Authors
  1. Steven G. Krantz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Steven G. Krantz.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Krantz, S.G. Uniqueness Properties of Hardy Space Functions. J Geom Anal 28, 253–264 (2018). https://doi.org/10.1007/s12220-017-9818-z

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12220-017-9818-z

Keywords

Mathematics Subject Classification

Search

Navigation