Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On certain integrals associated to CR-functions

Author: Telemachos Hatziafratis
Journal: Trans. Amer. Math. Soc. 314 (1989), 781-802
MSC: Primary 32A25
MathSciNet review: 958894
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Abstract: We construct explicit $ \bar \partial $-primitives of Cauchy-Fantappiè type kernels on analytic subvarieties of domains in $ {{\mathbf{C}}^n}$, outside the zero set of a holomorphic map defined on the variety. Then we use these primitives to derive, by means of a process of passing to a residue, integral formulas for $ {\text{CR}}$-functions defined on subsets of the boundary of a variety. Certain geometric restrictions on the varieties are imposed. These primitives apply in the particular case of the Bochner-Martinelli kernel in domains in $ {{\mathbf{C}}^n}$ and we use these primitives, in this case, to prove a criterion for holomorphic extendability of $ {\text{CR}}$-functions defined on certain subsets of the boundary of a domain in $ {{\mathbf{C}}^n}$.

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Article copyright: © Copyright 1989 American Mathematical Society