| Some properties of singular integral operators over an open curve Dedicated to the 85th birthday of Prof. Lu Jianke |
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| 作者姓名： | Yong-jia XU Guangdong University of Business Studies Guangzhou China |
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| 作者单位： | Yong-jia XU Guangdong University of Business Studies，Guangzhou 510320，China |
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| 基金项目： | the National Natural Science Foundation of China (Grant No. 10471048) |
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| 摘 要： | In this paper, the stability properties, the endpoint behavior and the invertible relations of Cauchy-type singular integral operators over an open curve are discussed. If the endpoints of the curve are not special, this type of operators are proved to be stable. At the endpoints, either the singularity or smoothness of the operators are exactly described. And the function sets or spaces on which the operators are invertible as well as the corresponding inverted operators are given. Meanwhile, some applications for the solution of Cauchy-type singular integral equations are illustrated.
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Some properties of singular integral operators over an open curve Dedicated to the 85th birthday of Prof. Lu Jianke |
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| Yong-jia XU Guangdong University of Business Studies,Guangzhou ,China.Some properties of singular integral operators over an open curve Dedicated to the 85th birthday of Prof. Lu Jianke[J].Science in China(Mathematics),2007(5). |
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| Authors: | Yong-jia XU Guangdong University of Business Studies Guangzhou China |
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| Institution: | Yong-jia XU Guangdong University of Business Studies,Guangzhou 510320,China |
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| Abstract: | In this paper, the stability properties, the endpoint behavior and the invertible relations of Cauchy-type singular integral operators over an open curve are discussed. If the endpoints of the curve are not special, this type of operators are proved to be stable. At the endpoints, either the singularity or smoothness of the operators are exactly described. And the function sets or spaces on which the operators are invertible as well as the corresponding inverted operators are given. Meanwhile, some applications for the solution of Cauchy-type singular integral equations are illustrated. |
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| Keywords: | stability endpoint behavior singular integral operator paired operators |
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