Siberian Mathematical Journal

, Volume 42, Issue 5, pp 952–960 | Cite as

One Boundary Version of Morera's Theorem

  • S. G. Myslivets


Let D be a bounded domain in Cn (n>1) with a connected smooth boundary ∂D and let f be a continuous function on ∂D. We consider conditions (generalizing those of the Hartogs–Bochner theorem) for holomorphic extendability of f to D. As a corollary we derive some boundary analog of Morera's theorem claiming that if the integrals of f vanish over the intersection of the boundary of the domain with complex curves in some class then f extends holomorphically to the domain.


Continuous Function Bounded Domain Smooth Boundary Holomorphic Extendability Boundary Analog 
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Copyright information

© Plenum Publishing Corporation 2001

Authors and Affiliations

  • S. G. Myslivets
    • 1
  1. 1.Krasnoyarsk State UniversityKrasnoyarsk

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