Geodesic
Boundary behaviour of holomorphic functions in Hardy–Sobolev spaces on convex domains in $\mathbb{C}^n$
Marco M. Peloso1 ; Hercule Valencourt1
1Dipartimento di Matematica Università degli Studi di Milano Via C. Saldini 50, 20133 Milano, Italy
Colloquium Mathematicum, Tome 118 (2010) no. 2, pp. 649-668
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/cm118-2-18
Keywords: study boundary behaviour holomorphic functions hardy sobolev spaces cal cal where cal smooth bounded convex domain finite type nbsp mathbb describing approach regions functions particular extend nbsp phenomenon first discovered nagel rudin shapiro the unit disk later extended sueiro strongly pseudoconvex domains

Marco M. Peloso  1   ; Hercule Valencourt  1

1 Dipartimento di Matematica Università degli Studi di Milano Via C. Saldini 50, 20133 Milano, Italy 
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Marco M. Peloso; Hercule Valencourt. Boundary behaviour of holomorphic functions in Hardy–Sobolev
spaces on convex domains in $\mathbb{C}^n$. Colloquium Mathematicum, Tome 118 (2010) no. 2, pp. 649-668. doi: 10.4064/cm118-2-18

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