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

### The Boundary Behavior of Isotonic Cauchy Type Integral in Clifford Analysis

Min KU1, Jin Yuan DU2, Dao Shun WANG1

1. 1. Department of Computer Science and Technology, Tsinghua University, Beijing 100084, P. R. China;
2. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, P. R. China
• Received:2009-07-08 Revised:2010-09-30 Online:2011-03-15 Published:2011-03-15

### Clifford鍒嗘瀽涓璉sotonic鏌タ鍨嬬Н鍒嗙殑杈圭晫鎬ц川

1. 1. 娓呭崕澶у璁＄畻鏈虹瀛︿笌鎶�鏈郴 鍖椾含 100084;
2. 姝︽眽澶у鏁板涓庣粺璁″闄� 姝︽眽 430072
• 鍩洪噾璧勫姪:

鍥藉863椤圭洰(2009AA011906);鍥藉鑷劧绉戝鍩洪噾璧勫姪椤圭洰(10871150,60873249);鍗氬＋鍚庡熀閲�(20090460316,201003111)

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.

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