This paper is mainly devoted to
the question about the holomorphic extendability on a domain D ⊂⊂Cn of the
CR-functions defined on a relatively open connected subset ∂D ∖K of ∂D. Pursuing
the investigation of our earlier paper proving that the 𝒪(D)-convexity of K suffices,
when n ≥ 2, for the desired extendability, here we obtain some further results on this
and similar matters, and a Hartogs’ type theorem for certain domains in a Levi-flat
hypersurface. All the results of this paper concern the case n ≥ 3 and fail to be true
in general for n = 2.
