Holomorphic continuation of functions from closed hypersurfaces with singular edges

We study the Bochner–Martinelli integral in a bounded domain $D$ in $\mathbb C^n$ whose boundary contains a finite number of singular edges. As an application we obtain generalizations of Hartogs–Bochner and Aizenberg–Kytmanov theorems on the holomorphic continuation of functions from the domain boundary into the domain.