Mathematical Notes

, Volume 79, Issue 5–6, pp 869–877 | Cite as

Continuation of separately analytic functions defined on part of a domain boundary

  • A. S. Sadullaev
  • S. A. Imomkulov


Suppose that D ⊂ ℂn is a domain with smooth boundary ∂D, E ⊂ ∂D is a boundary subset of positive Lebesgue measure mes(E) > 0, and FG is a nonpluripolar compact set in a strongly pseudoconvex domain G ⊂ ℂm. We prove that, under some additional conditions, each function separately analytic on the set X = (D×F)∪(E× G) can be holomorphically continued into the domain
where ω* is the P-measure and ω in * is the inner P-measure.

Key words

holomorphic function separately analytic function analytic continuation pseudoconvex domain pluripolar set Hartogs’ theorem 


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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • A. S. Sadullaev
    • 1
  • S. A. Imomkulov
    • 1
  1. 1.Urgench State UniversityRussia

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