biholomorphisms of strongly pseudoconvex domains extend to the boundary

It is a basic question in complex analysis to ask when does a biholomorphic mapping of two domains extend to the boundary. The following is a celebrated theorem of Fefferman for strongly pseudoconvex domains.

Theorem (Fefferman).

Let $U\mathrm{,}V\mathrm{\subset }{\mathrm{C}}^n$ ($n\mathrm{\ge }\mathrm{2}$) be two strongly pseudoconvex domains with smooth ($C^{\mathrm{\infty }}$) boundaries (the boundaries are smooth submanifolds). Let $f\mathrm{:}U\mathrm{\to }V$ be a biholomorphism.Then $f$ extends to a smooth diffeomorphism of $\overline{U}$ to $\overline{V}$.