SQUARE MEANS VERSUS DIRICHLET INTEGRALS FOR HARMONIC FUNCTIONS ON RIEMANN SURFACES

被引：0
|
作者：
Masaoka, Hiroaki [1 ]
Nakai, Mitsuru [1 ]
机构：
[1] Kyoto Sangyou Univ, Fac Sci, Dept Math, Kita Ku, Kyoto 6038555, Japan
来源：
TOHOKU MATHEMATICAL JOURNAL | 2012年 / 64卷 / 02期
关键词：
afforested surface; Dirichlet finite; Hardy space; Joukowski coordinate; mean bounded; Parreau decomposition; quasibounded; singular; Wiener harmonic boundary;
D O I：
10.2748/tmj/1341249373
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show rather unexpectedly and surprisingly the existence of a hyperbolic Riemann surface W enjoying the following two properties: firstly, the converse of the celebrated Parreau inclusion relation that the harmonic Hardy space H M-2(W) with exponent 2 consisting of square mean bounded harmonic functions on W includes the space H D(W) of Dirichlet finite harmonic functions on W, and a fortiori H M-2(W) = H D(W), is valid; secondly, the linear dimension of H M-2(W), hence also that of H D(W), is infinite.
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页码：233 / 259
页数：27
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