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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$.

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

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Keywords: Unit ball, Lie group, harmonic polynomials, principal series
Article copyright: © Copyright 1983 American Mathematical Society

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