Local boundary regularity of holomorphic mappings

Let f be a holomorphic mapping between two bounded domains D and D' in complex space ?ⁿ. Suppose that D and D' contain smooth real hypersurfaces Γ and Γ′ as open subsets of their respective boundaries, which correspond under a continuous extension of f. We shall show that this extension is smooth, given certain restrictions on Γ, Γ, and f.