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Some properties of a class of singular integral operators in Clifford analysis. (English) Zbl 1324.30091
Summary: This paper has two parts. In the first part, we study the boundedness and Hölder continuity for a class of singular integral operators, which are related to the Cauchy-type integrals of \(k\)-monogenic function in Clifford analysis. In the second part, we show the stability and error estimate of the singular integral operators when the boundary curve of integral domain \(\Omega\) perturbs.
MSC:
30E20 Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane
30E25 Boundary value problems in the complex plane
30G35 Functions of hypercomplex variables and generalized variables
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