Boundary behaviour of holomorphic functions in Hardy-Sobolev spaces on convex domains in $\Bbb C^n$

We study the boundary behaviour of holomorphic functions in the Hardy\u2013 Sobolev spaces Hp;k(D), where D is a smooth, bounded convex domain of finite type in Cn, by describing the approach regions for such functions. In particular, we extend a phenomenon first discovered by Nagel\u2013Rudin and Shapiro in the case of the unit disk, and later extended by Sueiro to the case of strongly pseudoconvex domains