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

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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


搴撴晱1, 鏉滈噾鍏�2, 鐜嬮亾椤�1   

  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:



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


鏈枃涓昏鍒荤敾浜嗗畾涔変簬鍋舵暟缁存姘忕┖闂翠腑鍏夋粦鏇查潰鑰屽彇鍊间簬澶岰lifford浠f暟鐨刬sotonic鏌タ鍨嬬Н鍒嗙殑杈圭晫鎬ц川. 瀵瑰叿鏈塇ölder瀵嗗害鍑芥暟鐨刬sotonic鏌タ鍨嬬Н鍒�,寰楀埌浜哖rivalov瀹氱悊鍜孲okhotskii--Plemelj鍏紡, 骞惰瘉鏄庝簡澶氬鍙樺嚱鏁拌涓粡鍏窧ochner--Martinelli鍨嬬Н鍒嗙殑Privalov瀹氱悊鍜孲okhotskii--Plemelj鍏紡涓哄叾鐗规畩鎯呭舰.


鍏抽敭璇�: Clifford鍒嗘瀽, Isotonic鏌タ鍨嬬Н鍒�, Privalov瀹氱悊, Plemelj鍏紡

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