| 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.
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| 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). |
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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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