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

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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 .

**[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*-*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*-*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)**

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

Article copyright:
© Copyright 1989
American Mathematical Society