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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Pluriharmonic functions in balls


Author: Walter Rudin
Journal: Proc. Amer. Math. Soc. 62 (1977), 44-46
MSC: Primary 32F05; Secondary 31C10
MathSciNet review: 0422687
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Abstract: It is proved that a function is pluriharmonic in the open unit ball of $ {{\mathbf{C}}^n}$ if and only if it is harmonic with respect to both the ordinary Laplacian and the invariant Laplace-Beltrami operator.


References [Enhancements On Off] (What's this?)

  • [1] R. C. Gunning and H. Rossi, Analytic functions of several complex variables, Prentice-Hall, Englewood Cliffs, N.J., 1965. MR 31 #4927. MR 0180696 (31:4927)
  • [2] E. M. Stein, Boundary behavior of holomorphic functions of several complex variables, Princeton Univ. Press, Princeton, N.J., 1972. MR 0473215 (57:12890)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0422687-7
PII: S 0002-9939(1977)0422687-7
Article copyright: © Copyright 1977 American Mathematical Society