Boundary behaviour of holomorphic functions in Hardy–Sobolev spaces on convex domains in $\mathbb{C}^n$

Volume 118 / 2010

Marco M. Peloso, Hercule Valencourt 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.

Authors

  • Marco M. PelosoDipartimento di Matematica
    Università degli Studi di Milano
    Via C. Saldini 50, 20133 Milano, Italy
    e-mail
  • Hercule ValencourtDipartimento di Matematica
    Università degli Studi di Milano
    Via C. Saldini 50, 20133 Milano, Italy
    e-mail

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