Nagoya Mathematical Journal

Variétés singulières et extension des fonctions holomorphes

Vincent Duquenoy and Emmanuel Mazzilli

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In this paper, we study a problem of extension of holomorphic functions given on a complex hypersurface with singularities on the boundary of a strictly pseudoconvex domain.

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Nagoya Math. J., Volume 192 (2008), 151-167.

First available in Project Euclid: 22 December 2008

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Zentralblatt MATH identifier

Primary: 32A27: Local theory of residues [See also 32C30] 32A37: Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) [See also 46Exx] 32C25: Analytic subsets and submanifolds 32C30: Integration on analytic sets and spaces, currents {For local theory, see 32A25 or 32A27}


Duquenoy, Vincent; Mazzilli, Emmanuel. Variétés singulières et extension des fonctions holomorphes. Nagoya Math. J. 192 (2008), 151--167.

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  • B. Berndtsson, The extension theorem of Ohsawa-Takegoshi and the theorem of Donnelly-Fefferman, Ann. Inst. Fourier, 4 (1996), 1083--1094.
  • P. Bonneau, A. Cumenge and A. Zeriahi, Division dans les espaces de Lipschitz de fonctions holomorphes, Lecture notes 1198, 1984.
  • K. Diederich and E. Mazzilli, A remark on the theorem of Ohsawa-Takagoshi, Nagoya Math. J., 158 (2000), 185--189.
  • G. Henkin, Continuation of bounded holomorphic functions from submanifold in general position to strictly pseudoconvex domains, Math. of the U\.S\.S\.R. Izvestija, 6 (1972), 536--563.
  • G. Henkin and M. Passare, Abelian differentials on singular varieties, Invent. Math., 135 (1999), 297--328.
  • A. Maati and E. Mazzilli, Extension et division dans les variétés à croisements normaux, Publ. Mat., 45 (2001), 343--369.
  • M. Passare, Residues, currents, and their relation to ideal of holomorphic functions, Math. Scand., 62 (1988), 75--152.
  • A. Tsikh, Multidimensional residues and their applications, Trans. of Math. Monogr 103, 1992.
  • A. Tsikh and A. Yger, Residue currents, J. Math. Sci., 120 (2004), 1916--1971.