Hostname: page-component-f554764f5-nt87m Total loading time: 0 Render date: 2025-04-09T21:54:27.151Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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