A Poisson-Jensen type representation formula for subharmonic functions on stratified Lie groups

被引：7

作者：

Bonfiglioli, A ^{[1
]}

Cinti, C ^{[1
]}

机构：

[1] Univ Bologna, Dipartimento Matemat, I-40126 Bologna, Italy

来源：

POTENTIAL ANALYSIS | 2005年 / 22卷 / 02期

关键词：

Poisson-Jensen representation formula; stratified Lie groups; sub-Laplacians; subharmonic functions; capacity; polar sets;

D O I：

10.1007/s11118-004-0588-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The aim of this paper is to prove a representation formula of Poisson - Jensen type on bounded domains Omega for subharmonic functions related to sub-Laplacians Delta(G) on stratified Lie groups G. Our result gives a complete answer to a question arisen in Math. Ann. 325 ( 2003), 97 122, where the additional hypothesis that Omega is regular for the Dirichlet problem related to Delta(G) was made: here we treat the case of arbitrary bounded domains Omega, omitting the hypothesis of regularity. In order to prove our representation formula, an ad-hoc theory of polar sets and capacity with respect to Delta(G) is also provided.

引用

页码：151 / 169

页数：19

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