One Boundary Version of Morera's Theorem

Author: Myslivets S.G.  

Publisher: Springer Publishing Company

ISSN: 0037-4466

Source: Siberian Mathematical Journal, Vol.42, Iss.5, 2001-09, pp. : 952-960

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Abstract

Let D be a bounded domain in C^n (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.