A CHARACTERIZATION OF POISSONIAN DOMAINS

被引：16

作者：

BISHOP, CJ

机构：

[1] Department of Mathematics, University of California, Los Angeles, Los Angeles, 90024, CA

来源：

ARKIV FOR MATEMATIK | 1991年 / 29卷 / 01期

关键词：

D O I：

10.1007/BF02384328

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a characterization of Poissonian domains in R(n), i.e., those domains for which every bounded harmonic function is the harmonic extension of some function in L infinity of harmonic measure. We deduce several properties of such domains, including some results of Mountford and Port. In two dimensions we give an additional characterization in terms of the logarithmic capacity of the boundary. We also give a necessary and sufficient condition for the harmonic measures on two disjoint planar domains to be mutually singular.

引用

页码：1 / 24

页数：24

共 30 条

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Ahlfors Lars V, 1979, COMPLEX ANAL

[2]

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

[3] AHLFORS AND CONFORMAL INVARIANTS [J].