Positive harmonic functions of finite order in a Denjoy type domain

被引：9

作者：

Aikawa, H ^{[1
]}

机构：

[1] Shimane Univ, Dept Math, Matsue, Shimane 6908504, Japan

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2003年 / 131卷 / 12期

关键词：

Denjoy type domain; harmonic function; finite order;

D O I：

10.1090/S0002-9939-03-06977-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce a Denjoy type domain and prove that the dimension of the cone of positive harmonic functions of finite order in the domain with vanishing boundary values is one or two, whenever the boundary is included in a certain set.

引用

页码：3873 / 3881

页数：9

共 15 条

[1] Norm estimate of Green operator, perturbation of Green function and integrability of superharmonic functions [J].

Aikawa, H .

MATHEMATISCHE ANNALEN, 1998, 312 (02) :289-318

[2] MARTIN BOUNDARY OF DENJOY DOMAINS [J].

ANCONA, A .

ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 1990, 15 (02) :259-271

[3]

ANCONA A, 1979, ANN I FOURIER GRENOB, V29, P71

[4]

Armitage D. H., 2001, SPRINGER MG MATH, DOI 10.1007/978-1-4471-0233-5

[5] POSITIVE HARMONIC-FUNCTIONS VANISHING ON THE BOUNDARY OF CERTAIN DOMAINS IN RN [J].

BENEDICKS, M .

ARKIV FOR MATEMATIK, 1980, 18 (01) :53-72

[6] MARTIN BOUNDARY OF A DOMAIN IN RN FOR WHICH THE BORDER IS INCLUDED IN A LIPSCHITZ HYPERSURFACE [J].

CHEVALLIER, N .

ARKIV FOR MATEMATIK, 1989, 27 (01) :29-48

[7] MARTIN BOUNDARIES OF SECTORIAL DOMAINS [J].

CRANSTON, MC ;

SALISBURY, TS .

ARKIV FOR MATEMATIK, 1993, 31 (01) :27-49

[8]

FRIEDLAND S, 1976, COMMENT MATH HELV, V51, P133

[9] MINIMAL HARMONIC-FUNCTIONS ON DENJOY DOMAINS [J].

GARDINER, SJ .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1989, 107 (04) :963-970

[10]

HAYMAN W. K., 1976, Subharmonic functions, V1

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