| 半空间中一类次调和函数的增长性质 |
| |
| 引用本文： | 张艳慧,邓冠铁.半空间中一类次调和函数的增长性质[J].数学学报,2008,51(2):319-326. |
| |
| 作者姓名： | 张艳慧 邓冠铁 |
| |
| 作者单位： | [1]首都师范大学数学系,北京100037 [2]北京工商大学数理系,北京100037 [3]北京师范大学数学系,北京100875 |
| |
| 基金项目： | 国家自然科学基金项目（10071005,10371011）;教育部留学回国人员科研启动基金项目;北京市教委科技发展计划资助项目 |
| |
| 摘 要： | 在Rn的半空间{x∈Rn,xn>0}中,得到了具有Dirichlet数据的Poisson积分在自然的积分收敛条件下满足增长性质u(x)=o(|x|),这里|x|→∞,这一性质对于半空间中满足一定条件的次调和函数仍然成立.该结果把复平面C中解析函数的增长性质推广到了n-维Euclidean半空间,并且推广了n-维Euclidean半空间中某些经典的结果.
|
| 关 键 词： | Poisson积分 次调和函数 增长性质 |
| 文章编号： | 0583-1431（2008）02-0319-08 |
| 收稿时间： | 2006-11-16 |
Growth Properties for a Class of Subharmonic Functions in Half Space |
| |
| Yah Hui ZHANG Guan Tie DENG.Growth Properties for a Class of Subharmonic Functions in Half Space[J].Acta Mathematica Sinica,2008,51(2):319-326. |
| |
| Authors: | Yah Hui ZHANG Guan Tie DENG |
| |
| Institution: | Yan Hui ZHANG Department of Mathematics, Capital Normal University, Beijing 100037, P. R. China Department of Mathematics and Physics, Beijing Technology and Business University, Beijing 100037, P. R. China Guan Tie DENG School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P. R. China |
| |
| Abstract: | We prove that the Poisson integral with Dirichlet data under the natural integral condition for convergence satisfying the growth property u(x) = o(|x|) when |x|→∞in Rn, and subharmonic functions of half space {x∈Rn, x > 0} with some conditions satisfy this growth property, too, which generalized the growth properties of anlytic functions in complex plane C to the n-dimentional Euclidean half space of Rn and some classic results of Rn. |
| |
| Keywords: | poisson integral subharmonic functions growth property |
| 本文献已被 维普 等数据库收录！ |
| 点击此处可从《数学学报》浏览原始摘要信息 |
| 点击此处可从《数学学报》下载免费的PDF全文 |
|
