Boundary behaviour of holomorphic functions in Hardy-Sobolev spaces on convex domains in ℂⁿ

Marco M. Peloso, and Hercule Valencourt. "Boundary behaviour of holomorphic functions in Hardy-Sobolev spaces on convex domains in ℂⁿ." Colloquium Mathematicae 118.2 (2010): 649-668. <http://eudml.org/doc/286417>.

@article{MarcoM2010,
abstract = {We study the boundary behaviour of holomorphic functions in the Hardy-Sobolev spaces $ℋ^\{p,k\}()$, where 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-Rudin and Shapiro in the case of the unit disk, and later extended by Sueiro to the case of strongly pseudoconvex domains.},
author = {Marco M. Peloso, Hercule Valencourt},
journal = {Colloquium Mathematicae},
keywords = {Hardy spaces; finite type domains; convex domains; approach regions},
language = {eng},
number = {2},
pages = {649-668},
title = {Boundary behaviour of holomorphic functions in Hardy-Sobolev spaces on convex domains in ℂⁿ},
url = {http://eudml.org/doc/286417},
volume = {118},
year = {2010},
}

TY - JOUR
AU - Marco M. Peloso
AU - Hercule Valencourt
TI - Boundary behaviour of holomorphic functions in Hardy-Sobolev spaces on convex domains in ℂⁿ
JO - Colloquium Mathematicae
PY - 2010
VL - 118
IS - 2
SP - 649
EP - 668
AB - We study the boundary behaviour of holomorphic functions in the Hardy-Sobolev spaces $ℋ^{p,k}()$, where 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-Rudin and Shapiro in the case of the unit disk, and later extended by Sueiro to the case of strongly pseudoconvex domains.
LA - eng
KW - Hardy spaces; finite type domains; convex domains; approach regions
UR - http://eudml.org/doc/286417
ER -