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高校应用数学学报
高校应用数学学报  2017, Vol. 32 Issue (2): 189-197    
    
Clifford分析中高阶$T$算子的$L^p$可积性
杨贺菊1 , 李尊凤2,1, 郭冰蟾2
1. 河北科技大学 理学院, 河北石家庄 050018
2. 河北师范大学 数学与信息科学学院, 河北石家庄 050024
$L^p$ intergrability of a higher order Teodorescu operator in Clifford analysis
YANG He-ju1 , LI Zun-feng1 , GUO Bing-chan2
1. College of Science, Hebei university of Science and Technology, Shijiazhuang 050018, China
2. College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050024, China
 全文: PDF 
摘要： 首先定义了定义于$\mathbf{R}^n$取值于$A_n(R)$的高阶$T$算子并讨论了它在$L^\gamma$空间中的性质. 其次, 估计了$T$算子的模, 并引入了修正的高阶Teodorescu算子$T^*$. 接下来, 根据Banach压缩映射原理证明了算子$T^*$存在唯一的不动点. 最后, 证明了Mann迭代序列强收敛于$T^*$的不动点, 进而给出了一个奇异积分方程解的迭代序列.
关键词： Clifford分析;  Teodorescu算子;  不动点定理;  Mann迭代序列    
Abstract: Firstly, the $A_n(R)$-valued higher order Teodorescu operator $T$ in $\mathbf{R}^n$ is defined and its properties in $L^\gamma$ space are discussed. Secondly, its norm is estimated and a modified higher order Teodorescu operator $T^*$ is introduced. And then, that the operator $T^*$ has a unique fixed point by the Banach’s contract mapping principle is proved. Finally, that the Mann iterative sequence strongly converges to the fixed point of $T^*$ is proved and an iterative sequence of the solution of a singular integral equation is given.
Key words: Clifford analysis    Teodorescu operator    fixed point theorem    Mann iterative sequence
收稿日期: 2016-10-28 出版日期: 2017-06-01
基金资助: 国家自然科学基金(11401159; 11571089; 11301136; 11401162); 河北省自然科学基金(A2016205218; A2014208158; A2014205069; A2015205012); 河北师范大学博士基金(L2015B04; L2015B03)
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引用本文:

杨贺菊, 李尊凤, 郭冰蟾. Clifford分析中高阶$T$算子的$L^p$可积性[J]. 高校应用数学学报, 2017, 32(2): 189-197.

YANG He-ju , LI Zun-feng , GUO Bing-chan. $L^p$ intergrability of a higher order Teodorescu operator in Clifford analysis. Applied Mathematics A Journal of Chinese Universities, 2017, 32(2): 189-197.

链接本文:

http://www.zjujournals.com/amjcua/CN/    或    http://www.zjujournals.com/amjcua/CN/Y2017/V32/I2/189

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