AN INVARIANT VOLUME-MEAN-VALUE PROPERTY

被引：72

作者：

AHERN, P ^{[1
]}

FLORES, M ^{[1
]}

RUDIN, W ^{[1
]}

机构：

[1] UNIV LA LAGUNA,E-38771 LA LAGUNA,SPAIN

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 1993年 / 111卷 / 02期

关键词：

D O I：

10.1006/jfan.1993.1018

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

If f(hook) is harmonic and integrable over the open unit disc U then so is f(hook) (ring operator) ψ for every Moebius transformation ψ of U, and therefore 1 π ∫ U (f(hook) (ring operator) ψ) d A = f(hook)(ψ(0) for every ψ. Conversely, does this mean-value property imply that f(hook) is harmonic? A more general question, with the unit ball Bn of C (for arbitrary n≥ 1) in place of the disc, is investigated in the present paper. The answer is found to be affirmative if n ≤ 11, negative if n ≤ 12. © 1993 Academic Press Inc.

引用

页码：380 / 397

页数：18