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THE MEAN-VALUE PROPERTY AND (α,β)-HARMONICITY

Part of: Higher-dimensional theory

Published online by Cambridge University Press:  14 October 2011

DAN LI  and
CONGWEN LIU
DAN LI*
Affiliation:
Chern Institute of Mathematics, Nankai University, Tianjin 300071, PR China (email: [email protected])
CONGWEN LIU
Affiliation:
School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, PR China (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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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.

Keywords

(α,β)-harmonic functionsBerezin-type transformsmean-value property

MSC classification

Secondary: 31B05: Harmonic, subharmonic, superharmonic functions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 91 , Issue 2 , October 2011 , pp. 189 - 206
Copyright
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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