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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Differentiability criteria and harmonic functions on $B^{n}$
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by Patrick R. Ahern and Kenneth D. Johnson PDF
Proc. Amer. Math. Soc. 89 (1983), 709-712 Request permission

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
  • © Copyright 1983 American Mathematical Society
  • 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