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.

引用

页码：233 / 259

页数：27

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