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Some properties of singular integral operators over an open curve

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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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Authors and Affiliations

  1. Guangdong University of Business Studies, Guangzhou, 510320, China

    Yong-jia Xu

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  1. Yong-jia Xu
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Additional information

Dedicated to the 85th birthday of Prof. Lu Jianke

This work was partially supported by the National Natural Science Foundation of China (Grant No. 10471048)

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Xu, Yj. Some properties of singular integral operators over an open curve. SCI CHINA SER A 50, 628–650 (2007). https://doi.org/10.1007/s11425-007-0022-7

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  • DOI: https://doi.org/10.1007/s11425-007-0022-7

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