| 半平面中调和函数的积分表示 |
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| 引用本文： | 邓冠铁.半平面中调和函数的积分表示[J].数学杂志,2006,26(6):682-684. |
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| 作者姓名： | 邓冠铁 |
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| 作者单位： | 北京师范大学数学系,北京,100875 |
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| 基金项目： | 国家自然科学基金资助项目(10371011,10071005)，教育部留学回国人员科研启动基金资助项目. |
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| 摘 要： | 本文对于半平面中的调和函数u(z),证明了正部u (z)满足某些限制增长条件,用半平面边界上的积分表示,它的负部u-(z)也被类似的增长条件所控制.得到了半平面中负的调和函数的经典结果.
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| 关 键 词： | 调和函数 积分表示 Nevanlinna公式 |
| 文章编号： | 0255-7797（2006）06-0682-03 |
| 收稿时间： | 2004-09-16 |
| 修稿时间： | 2004-09-162005-01-24 |
INTEGRAL REPRESENTATION OF HARMONIC FUNCTIONS IN A HALF PLANE |
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| DENG Guan-tie.INTEGRAL REPRESENTATION OF HARMONIC FUNCTIONS IN A HALF PLANE[J].Journal of Mathematics,2006,26(6):682-684. |
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| Authors: | DENG Guan-tie |
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| Institution: | Dept. of Math., Beijing Normal University, Beijing 100875, China |
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| Abstract: | In this paper, we prove that a harmonic function u(z) in a half plane, in case its positive part u (z) satisfying a slowly growing condition, can be represented by its integral on the boundary of the half plane and that its negative part u-(z) can be dominated by a similar slowly growing condition. For a negative harmonic function in a half plane, our result is some classical one about harmonic functions in a half-plane. |
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| Keywords: | harmonic function integral representation Nevanlinna formula |
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