The Boundary Behavior of Isotonic Cauchy Type Integral in Clifford Analysis

Min KU, Jin Yuan DU, Dao Shun WANG

Acta Mathematica Sinica, Chinese Series ›› 2011, Vol. 54 ›› Issue (2) : 177-186.

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Acta Mathematica Sinica, Chinese Series ›› 2011, Vol. 54 ›› Issue (2) : 177-186. DOI: 10.12386/A2011sxxb0019
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The Boundary Behavior of Isotonic Cauchy Type Integral in Clifford Analysis

  • Min KU1, Jin Yuan DU2, Dao Shun WANG1
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Abstract

The holomorphic functions of several complex variables are closely related to the so-called isotonic Dirac system in which different Dirac operators in the half dimension act from the left and from the right on the functions considered. In this paper we mainly study the boundary properties of the isotonic Cauchy type integral operator over the smooth surface in Euclidean space of even dimension with values in a complex Clifford algebra. We obtain Privalov theorem inducing Sokhotskii-Plemelj formula as the special case for the isotonic Cauchy type integral operator with Hölder density functions taking values in a complex Clifford algebra, and show that Privalov theorem of the classical Bochner-Martinelli type integral and the classical Sokhotskii- Plemelj formula over the smooth surface of Euclidean space for holomorphic functions of several complex variables may be derived from it.

 

Key words

Clifford analysis / Isotonic Cauchy type integral / Privalov theorem

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Min KU, Jin Yuan DU, Dao Shun WANG. The Boundary Behavior of Isotonic Cauchy Type Integral in Clifford Analysis. Acta Mathematica Sinica, Chinese Series, 2011, 54(2): 177-186 https://doi.org/10.12386/A2011sxxb0019

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