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

Differentiability criteria and harmonic functions on $ B\sp{n}$


Authors: Patrick R. Ahern and Kenneth D. Johnson
Journal: Proc. Amer. Math. Soc. 89 (1983), 709-712
MSC: Primary 43A85; Secondary 22E30, 31B05, 33A75
MathSciNet review: 719001
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Abstract: Let $ {B^n}$ be the unit ball in $ {{\mathbf{F}}^n}$ where $ {\mathbf{F}}$ is either $ {\mathbf{R}}$, $ {\mathbf{C}}$ or $ {\mathbf{H}}$. The space $ {B^n}$ is a classical rank one symmetric space with respect to the action of a Lie group $ G$. Suppose $ f$ is a $ G$-harmonic function on $ {B^n}$ all of whose derivatives of order $ \leqslant k$ are bounded. Our main result obtains restrictions on $ f$ depending on $ k$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0719001-9
PII: S 0002-9939(1983)0719001-9
Keywords: Unit ball, Lie group, harmonic polynomials, principal series
Article copyright: © Copyright 1983 American Mathematical Society