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$${L^p}$$ integrability of a higher order Teodorescu operator in Clifford analysis. (Chinese. English summary) Zbl 1389.30160
Summary: Firstly, the $$A_n\left(R \right)$$-valued higher order Teodorescu operator $$T$$ in $$\mathbb R^n$$ 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.
##### MSC:
 30G35 Functions of hypercomplex variables and generalized variables
##### Keywords:
Clifford analysis; Teodorescu operator; fixed point theorem