Integral representations of harmonic functions in half spaces
Integral representations of harmonic functions in half spaces
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DOI：
10.1016/j.bulsci.2006.03.008
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发表时间：
2007
影响因子：
1.3
通讯作者：
Guantie Deng
中科院分区：
文献类型：
--
作者：
Guantie Deng
In this paper, using a modified Poisson kernel in an upper half-space, we prove that a harmonic function u(z) in a upper half space with its positive part u+(x)=max{u(x),0} satisfying a slowly growing condition can be represented by its integral in the boundary of the upper half space, the integral representation is unique up to the addition of a harmonic polynomial, vanishing in the boundary of the upper half space and that its negative part u−(x)=max{−u(x),0} can be dominated by a similar slowly growing condition, this improves some classical result about harmonic functions in the upper half space.
