Boundary behaviour of holomorphic functions in Hardy–Sobolev spaces on convex domains in $\mathbb{C}^n$
Volume 118 / 2010
Colloquium Mathematicum 118 (2010), 649-668
MSC: 32A35, 32T25, 46E22.
DOI: 10.4064/cm118-2-18
Abstract
We study the boundary behaviour of holomorphic functions in the Hardy–Sobolev spaces ${\cal H}^{p,k}({\cal D})$, where $\cal D$ is a smooth, bounded convex domain of finite type in $\mathbb C^n$, by describing the approach regions for such functions. In particular, we extend a phenomenon first discovered by Nagel–Rudin and Shapiro in the case of the unit disk, and later extended by Sueiro to the case of strongly pseudoconvex domains.
