Journal of Mathematical Sciences

, Volume 87, Issue 5, pp 3925–3940 | Cite as

Estimates of the Bergman kernel for some pseudoconvex domains

  • N. A. Shirokov


Denote by Kω(z, ζ) the Bergman kernel of a pseudoconvex domain Ω. For some classes of domains Ω, a relationship is found between the rate of increase of Kω(z, z) as z tends to ∂Ω, and a purely geometric property of Ω. Bibliography: 5 titles.


Geometric Property Pseudoconvex Domain Bergman Kernel 
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Literature Cited

  1. 1.
    Ch. Fefferman, “The Bergman kernel and biholomorphic mappings of pseudoconvex domains,”Invent. Math.,26, 1–65 (1974).CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    A. Bonami and N. Lohoué, “Projectures de Bergman et Szegö pour une classe de domains faiblement pseudo-convexes et estimationL p,”Comp. Math.,46, 159–226 (1982).Google Scholar
  3. 3.
    N. A. Shirokov, “The Bergman kernel near the diagonal for domains close to ellipsoids,”Zap. Mauchn. Semin. POMI,190, 163–172 (1991).MATHGoogle Scholar
  4. 4.
    G. M. Henkin and J. Leiterer,Theory of Functions on Complex Manifolds, Academie-Verlag, Berlin (1984).Google Scholar
  5. 5.
    N. A. Shirokov, “The Jackson-Bernstein theorem for strictly convex domains in ℂn,”Dokl. Akad. Nauk SSSR,276, 1079–1081 (1984).MATHMathSciNetGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • N. A. Shirokov

There are no affiliations available

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