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M-harmonic functions with M-harmonic square

Published online by Cambridge University Press:  17 April 2009

Hong Oh Kim
Hong Oh Kim
Affiliation:
Department of Mathematics, Korea Advanced Institute of Science and Technology, 373–1 Kusong-Dong Yusong-GuTaejon 3–5–701Kores
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ℳ-harmonic functions with ℳ-harmonic square are proved to be either holomorphic or antiholomorphic in the unit ball of complex n-space under certain additional conditions. For example, if u and u2 are ℳ-harmonic in the unit ball of ℂ2 and if u is continuously differentiable up to the boundary then u is either holomorphic or antiholomorphic.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 53 , Issue 1 , February 1996 , pp. 123 - 129
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Ahern, P.R. and Rudin, Walter, ‘ℳ-harmonic products’, Indag. Math. 2 (1991), 141–147.CrossRefGoogle Scholar
[2]Folland, G.B., ‘Spherical harmonic expansion of the Poission-Szago kernel for the ball’, Proc. Amer. Math. Soc. 47 2 (1975), 401 – 408.Google Scholar
[3]Rudin, Walter, Function theory in the unit ball of ℂn (Springer-Verlag, Berlin, Heidelberg, New York, 1980).CrossRefGoogle Scholar