Remote Access Transactions of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9947-1989-0958894-7
MathSciNet review: 958894
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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}$.


References [Enhancements On Off] (What's this?)

  • [1] I. Aizenberg and A. Yuzhakov, Integral representations and residues in multidimensional complex analysis, Transl. Math. Monos., vol. 58, Amer. Math. Soc., Providence, R.I., 1983. MR 735793 (85a:32006)
  • [2] T. Hatziafratis, Integral representation formulas on analytic varieties, Pacific J. Math. 123 (1986), 71-91. MR 834139 (87e:32004)
  • [3] G. Lupacciolu, A theorem on holomorphic extension of $ CR$-functions, Pacific J. Math. 124 (1986), 177-191. MR 850675 (87k:32026)
  • [4] -, Holomorphic continuation in several complex variables, Pacific J. Math. 128 (1987), 117-126. MR 883380 (88f:32050)
  • [5] G. Lupacciolu and G. Tomassini, Un teorema di estensione per le $ CR$-funzioni, Ann. Mat. Pura Appl. 137 (1984), 257-263. MR 772261 (86e:32021)
  • [6] E. L. Stout, An integral formula for holomorphic functions on strictly pseudoconvex hypersurfaces, Duke Math. J. 42 (1975), 347-356. MR 0369731 (51:5963)
  • [7] -, Analytic continuation and boundary continuity of functions of several complex variables, Proc. Roy. Soc. Edinburgh 89A (1981), 63-74. MR 628129 (83c:32021)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 32A25

Retrieve articles in all journals with MSC: 32A25


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1989-0958894-7
Article copyright: © Copyright 1989 American Mathematical Society

American Mathematical Society