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 -primitives of Cauchy-Fantappiè type kernels on analytic subvarieties of domains in , 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 -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 and we use these primitives, in this case, to prove a criterion for holomorphic extendability of -functions defined on certain subsets of the boundary of a domain in .

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DOI:
http://dx.doi.org/10.1090/S0002-9947-1989-0958894-7

Article copyright:
© Copyright 1989
American Mathematical Society