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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Differentiability criteria and harmonic functions on $B^{n}$


Authors: Patrick R. Ahern and Kenneth D. Johnson
Journal: Proc. Amer. Math. Soc. 89 (1983), 709-712
MSC: Primary 43A85; Secondary 22E30, 31B05, 33A75
DOI: https://doi.org/10.1090/S0002-9939-1983-0719001-9
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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Keywords: Unit ball, Lie group, harmonic polynomials, principal series
Article copyright: © Copyright 1983 American Mathematical Society