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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
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