Some boundary increasing properties of harmonic functions in Lipschitz domain

被引：0

作者：

Zhang, YP ^{[1
]}

机构：

[1] WUHAN UNIV, DEPT MATH, WUHAN 430072, PEOPLES R CHINA

来源：

CHINESE ANNALS OF MATHEMATICS SERIES B | 1996年 / 17卷 / 02期

关键词：

Martin representation; harmonic function; harmonic measure;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The object of this paper is to study the non-tangential increasing properties of positive harmonic function u in Lipschitz domain by means of Martin representation theory. A necessary and sufficient condition of the control of growth of u near any fixed boundary point is obtained. It is shown that the non-tangential increasing degree of u near a boundary point is exactly the local degree of its representation measure with respect to the harmonic measure. Some examples are given.

引用

页码：159 / 166

页数：8

共 50 条

[21] An approximation property of harmonic functions in Lipschitz domains and some of its consequences
Rivera-Noriega, J
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2004, 132 (05) : 1321 - 1331
[22] ON INFINITE NONTANGENTIAL BOUNDARY-VALUES OF FUNCTIONS, SUBHARMONIC IN A LIPSCHITZ DOMAIN
GOLUZINA, MG
MATHEMATICAL NOTES, 1994, 55 (1-2) : 93 - 95
[23] Boundary behaviour of p-harmonic functions in domains beyond Lipschitz domains
Lewis, John L.
Nystrom, Kaj
ADVANCES IN CALCULUS OF VARIATIONS, 2008, 1 (02) : 133 - 170
[24] Some Properties of General Fourier Coefficients of Lipschitz Functions
V. Tsagareishvili
Analysis Mathematica, 2021, 47 : 229 - 241
[25] Some Properties of General Fourier Coefficients of Lipschitz Functions
Tsagareishvili, V.
ANALYSIS MATHEMATICA, 2021, 47 (01) : 229 - 241
[26] BOUNDARY PROPERTIES OF MINIMAL HARMONIC-FUNCTIONS
KEMPER, JT
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1976, 60 (OCT) : 193 - 196
[27] POSITIVE HARMONIC FUNCTIONS ON LIPSCHITZ DOMAINS
HUNT, RA
WHEEDEN, RL
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1970, 147 (02) : 507 - &
[28] Discrete harmonic functions in Lipschitz domains
Mustapha, Sami
Sifi, Mohamed
ELECTRONIC COMMUNICATIONS IN PROBABILITY, 2019, 24
[29] LIPSCHITZ APPROXIMATION BY HARMONIC-FUNCTIONS AND SOME APPLICATIONS TO SPECTRAL-SYNTHESIS
MATEU, J
OROBITG, J
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1990, 39 (03) : 703 - 736
[30] WEIGHTED NORM INEQUALITIES FOR THE LUSIN AREA INTEGRAL AND THE NONTANGENTIAL MAXIMAL FUNCTIONS FOR FUNCTIONS HARMONIC IN A LIPSCHITZ DOMAIN
DAHLBERG, BEJ
STUDIA MATHEMATICA, 1980, 67 (03) : 297 - 314

← 1 2 3 4 5 →