Abstract
In this paper, we obtain a higher order derivative formula of the solid Cauchy integral operator on smooth bounded domains in \({\mathbb {C}}\). The formula can be used to prove a Calderón–Zygmund type theorem for higher order singular integrals, and to obtain a criterion for the solvability of the \({{\bar{\partial }}}\) problem in the flat category.
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Acknowledgements
The authors wish to thank the anonymous referee for providing valuable comments and suggestions on the paper. The work was done while the first author visited the Department of Mathematical Sciences at Purdue University Fort Wayne. He also thanks the department for the hospitality.
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The research leading to these results received funding from NNSF of China under Grant 11671361, and from NSF under Grant DMS 1501024.
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The first author was partially supported by the NNSF of China under Grant 11671361 and China Scholarship Council (CSC). The third author was partially supported by the NSF Grant DMS 1501024.
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Liu, Y., Pan, Y. & Zhang, Y. A Derivative Formula for the Solid Cauchy Integral Operator and Its Applications. Integr. Equ. Oper. Theory 94, 38 (2022). https://doi.org/10.1007/s00020-022-02717-0
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DOI: https://doi.org/10.1007/s00020-022-02717-0