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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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On certain integrals associated to CR-functions
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by Telemachos Hatziafratis PDF
Trans. Amer. Math. Soc. 314 (1989), 781-802 Request permission

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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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 314 (1989), 781-802
  • MSC: Primary 32A25
  • DOI: https://doi.org/10.1090/S0002-9947-1989-0958894-7
  • MathSciNet review: 958894