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THE MEAN-VALUE PROPERTY AND (α,β)-HARMONICITY
Published online by Cambridge University Press: 14 October 2011
Abstract
In this article we consider whether, for integrable functions on the unit ball of ℂn, the mean-value property implies (α,β)-harmonicity. We find that the answer is affirmative when 0<n+α+β≤ρ0, but is negative when n+α+β>ρ0. Here ρ0 is a constant between 11.025 and 11.069.
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- Research Article
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- Copyright © Australian Mathematical Publishing Association Inc. 2011
Footnotes
This work was supported by the National Natural Science Foundation of China (No. 10601025, 11071230) and the Anhui Provincial Natural Science Foundation (No. 090416233).
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