|本期目录/Table of Contents|

[1]龚 定 东.广义上半空间的CauchyFantappié型奇异积分[J].厦门大学学报(自然科学版),2012,51(5):813.
 GONG Ding dong.Singular Integrals of CauchyFantappié Type on the Generalized Upper Half Space[J].Journal of Xiamen University(Natural Science),2012,51(5):813.
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广义上半空间的CauchyFantappié型奇异积分(PDF)
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《厦门大学学报(自然科学版)》[ISSN:0438-0479/CN:35-1070/N]

卷:
51卷
期数:
2012年第5期
页码:
813
栏目:
研究论文
出版日期:
2012-09-20

文章信息/Info

Title:
Singular Integrals of CauchyFantappié Type on the Generalized Upper Half Space
作者:
龚 定 东
浙江理工大学数学科学系,浙江 杭州 310018
Author(s):
GONG Dingdong
Department of Mathematical Sciences,Zhejiang SciTech University,Hangzhou 310018,China
关键词:
广义上半空间CauchyFantappié型核奇异积分Plemelj公式
Keywords:
generalized upper half spaceCauchyFantappi kernelsingular integralPlemelj formula
分类号:
O 174.56
文献标志码:
-
摘要:
Cn(n>1)中的广义上半空间是一特殊的无界域.本文利用广义上半空间上的全纯的CauchyFantappié核研究了Cauchy型积分的边界行为,得到了奇异积分的Cauchy主值的存在性.此处Cauchy型积分的密度函数是一类特殊的Hlder函数. 进一步研究了Cauchy型积分的边界极限值,得到了Plemelj 公式.广义上半空间中Cauchy型积分在无穷远点处的边界行为的处理是无界域情形特有的.
Abstract:
The generalized upper half space in Cn(n>1) is an unbounded domain. In this paper by using the holomorphic CauchyFantappié kernel of the generalized upper half space the boundary behavior of the Cauchy type integral on the generalized upper half space is studied, and the existence of the principal value of the singular integral is obtained. The density functions in the Cauchy type integral are a kind of special Hlder functions. The boundary limit value of the Cauchy type integral is further studied, and Plemelj formula is obtained.The operation on the boundary behavior at the infinity point in the Cauchy type integral on the generalized upper half space is peculiar to the case of the unbounded domain.

参考文献/References:


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备注/Memo

备注/Memo:
收稿日期:20120305 基金项目:国家自然科学基金项目(11171298);浙江省自然科学基金项目(Y6110425);浙江理工大学科研启动基金项目(0913841Y) Email:ddgong@zstu.edu.cn
更新日期/Last Update: 2012-09-20