Some Properties of Cauchy-type Singular Integral Operator on Unbounded Domains
Received:July 08, 2013  Revised:February 24, 2014
Key Words: regular function   Cauchy-type singular integral operator   unbounded domains   H\"{o}lder continuity.  
Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.11401162;11301136) and the Science Foundation of Hebei Province (Grant No.A2014208158).
Author NameAffiliation
Liping WANG College of Mathematics and Information Science, Hebei Normal University, Hebei 050024, P. R. China 
Yuying QIAO College of Mathematics and Information Science, Hebei Normal University, Hebei 050024, P. R. China 
Weiping ZHANG College of Mathematics and Information Science, Hebei Normal University, Hebei 050024, P. R. China 
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Abstract:
      On the basis of introducing the modified Cauchy kernel, we discuss the H\"{o}lder continuity of the Cauchy-type singular integral operator on unbounded domains for regular functions by dividing into the following three cases: two points are on the boundary of region; one point is on the boundary and another point is in the interior(or exterior) of the region; two points are in the interior (or exterior) of the region.
Citation:
DOI:10.3770/j.issn:2095-2651.2014.05.008
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