A Derivative Formula for the Solid Cauchy Integral Operator and Its Applications

In this paper, we obtain a higher order derivative formula of the solid Cauchy integral operator on smooth bounded domains in 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 ∂ ¯ problem in...

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Bibliographic Details
Published in:Integral equations and operator theory 2022-12, Vol.94 (4), Article 38
Main Authors: Liu, Yang, Pan, Yifei, Zhang, Yuan
Format: Article
Language:English
Subjects:
Analysis
Derivatives
Integrals
Mathematics
Mathematics and Statistics
Operators (mathematics)
Citations: Items that this one cites
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Summary:In this paper, we obtain a higher order derivative formula of the solid Cauchy integral operator on smooth bounded domains in 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 ∂ ¯ problem in the flat category.
ISSN:0378-620X
1420-8989
DOI:10.1007/s00020-022-02717-0