On a boundary version of Morera's theorem

Let $D$ be a bounded domain in $\mathbb C^n(n>1)$ with a connected smooth boundary $\partial D$ and let $f$ a continuous function on $\partial D$. 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.