Real analytic boundary regularity of the Cauchy kernel on convex domains
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- by So-Chin Chen PDF
- Proc. Amer. Math. Soc. 108 (1990), 423-432 Request permission
Abstract:
It is well-known that in one complex variable the Cauchy integral preserves real analyticity near the boundary. In this paper we show that the same conclusion also holds on convex domains with real analytic boundary in higher dimension, where the Cauchy kernel is given by the Cauchy-Fantappiè form of order zero generated by the (l.0)-form $C\left ( {\xi ,z} \right )$, \[ C\left ( {\xi ,z} \right ) = \left ( {\sum \limits _{j = 1}^n {\frac {{\partial r}}{{\partial {\xi _j}}}} \left ( \xi \right )d{\xi _j}} \right ){\left ( {\sum \limits _{j = 1}^n {\frac {{\partial r}}{{\partial {\xi _j}}}} \left ( \xi \right )\left ( {{\xi _j} - {z_j}} \right )} \right )^{ - 1}},\] where $r\left ( \xi \right )$ is the defining function of the domain.References
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Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 108 (1990), 423-432
- MSC: Primary 32A25; Secondary 32A40, 32F15
- DOI: https://doi.org/10.1090/S0002-9939-1990-1000149-2
- MathSciNet review: 1000149