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

• Autorzy: Marco M. Peloso , Hercule Valencourt
• Języki publikacji: EN

Abstrakty

EN

We study the boundary behaviour of holomorphic functions in the Hardy-Sobolev spaces $ℋ^{p,k}(𝓓)$, 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-Rudin and Shapiro in the case of the unit disk, and later extended by Sueiro to the case of strongly pseudoconvex domains.

Kategorie tematyczne

• 46E22: Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)
• 32A35: H p -spaces, Nevanlinna spaces
• 32T25: Finite type domains

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2010
• Tom: 118
• Numer: 2
• Strony: 649-668

Daty

wydano

2010

Twórcy

autor

Marco M. Peloso

• Dipartimento di Matematica, Università degli Studi di Milano, Via C. Saldini 50, 20133 Milano, Italy

autor

Hercule Valencourt

• Dipartimento di Matematica, Università degli Studi di Milano, Via C. Saldini 50, 20133 Milano, Italy

Identyfikatory

DOI

10.4064/cm118-2-18