Holomorphic continuation of functions in the domains with singular boundaries

We consider bounded domains <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper D"> <mml:semantics> <mml:mi>D</mml:mi> <mml:annotation encoding="application/x-tex">D</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-struck upper C Superscript n"> <mml:semantics> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">C</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> <mml:annotation encoding="application/x-tex">\mathbb C^n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> , which boundary contains the finite number of singular wedges. In those domains the boundary behavior of the Bochner-Martinelli integral is investigated. As an application we obtain theorems on the holomorphic continuation of functions from the boundary of the domains into the domain, which generalizes the Hartogs-Bochner theorem and the Aizenberg-Kytmanov theorem.

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