Duke Mathematical Journal

The pointwise Fatou theorem and its converse for positive pluriharmonic functions

Wade Ramey and David Ullrich

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Article information

Source
Duke Math. J., Volume 49, Number 3 (1982), 655-675.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1077315383

Digital Object Identifier
doi:10.1215/S0012-7094-82-04934-1

Mathematical Reviews number (MathSciNet)
MR672501

Zentralblatt MATH identifier
0558.31002

Subjects
Primary: 32A25: Integral representations; canonical kernels (Szego, Bergman, etc.)
Secondary: 31C10: Pluriharmonic and plurisubharmonic functions [See also 32U05]

Citation

Ramey, Wade; Ullrich, David. The pointwise Fatou theorem and its converse for positive pluriharmonic functions. Duke Math. J. 49 (1982), no. 3, 655--675. doi:10.1215/S0012-7094-82-04934-1. https://projecteuclid.org/euclid.dmj/1077315383


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References

  • [1] P. Fatou, Series trigonometriques et series de Taylor, Acta Mathematica 30 (1906), 335.
  • [2] L. L. Helms, Introduction to potential theory, Pure and Applied Mathematics, Vol. XXII, Wiley-Interscience A Division of John Wiley & Sons, New York-London-Sydney, 1969.
  • [3] A. Korányi, Harmonic functions on Hermitian hyperbolic space, Trans. Amer. Math. Soc. 135 (1969), 507–516.
  • [4] L. H. Loomis, The converse of the Fatou theorem for positive harmonic functions, Trans. Amer. Math. Soc. 53 (1943), 239–250.
  • [5] W. Rudin, Tauberian theorems for positive harmonic functions, Nederl. Akad. Wetensch. Indag. Math. 40 (1978), no. 3, 376–384.
  • [6] W. Rudin, Function theory in the unit ball of $\bf C\spn$, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Science], vol. 241, Springer-Verlag, New York, 1980.
  • [7] E. M. Stein, Boundary behavior of holomorphic functions of several complex variables, Princeton University Press, Princeton, N.J., 1972.