Clifford分析中高阶T算子的L^p可积性

L^p intergrability of a higher order Teodorescu operator in Clifford analysis

首先定义了定义于R^n取值于A_n(R)的高阶T算子并讨论了它在Lγ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.

Firstly, the An（R）-valued higher order Teodorescu operator T in Rn is defined and its properties in L-γ 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.