Abstract
Let \({\Omega }\) be a smoothly bounded, convex domain in \(\mathbb {C}^{2}\), satisfying the maximal type \(F\). In this paper, we consider the boundary Lipschitz regularity and Gevrey regularity of the Cauchy transform \(\mathcal {C}[u]\) on \({\Omega }\), with an application of the Henkin operator for \(\bar {\partial }\)-equation. Here, the notion of maximal type \(F\) contains all domains of strictly finite type and many cases of infinite type in the sense of Range.
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Acknowledgements
This article was written while the author was a visiting member at the Vietnam Institute for Advanced Study in Mathematics (VIASM), Hanoi, Summer 2016. He would like to thank this institution for its hospitality and support. The author is grateful to the referee(s) for careful reading of the paper and valuable suggestions and comments.
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This research is funded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.02-2017.06.
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Ha, L.K. The Cauchy Transform and Henkin Operator on Convex Domains of Maximal Type \(F\) in \(\mathbb {C}^{2}\). Vietnam J. Math. 47, 209–225 (2019). https://doi.org/10.1007/s10013-018-0286-y
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DOI: https://doi.org/10.1007/s10013-018-0286-y