On propagation of boundary continuity of holomorphic functions of several variables

Salla Franzén; Burglind Jöricke

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2008)

  • Volume: 7, Issue: 2, page 271-285
  • ISSN: 0391-173X

Abstract

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We prove that continuity properties of bounded analytic functions in bounded smoothly bounded pseudoconvex domains in two-dimensional affine space are determined by their behaviour near the Shilov boundary. Namely, if the function has continuous extension to an open subset of the boundary containing the Shilov boundary it extends continuously to the whole boundary. If it is e.g. Hölder continuous on such a boundary set, it is Hölder continuous on the closure of the domain. The statements may fail if the boundary is not smooth.

How to cite

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Franzén, Salla, and Jöricke, Burglind. "On propagation of boundary continuity of holomorphic functions of several variables." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 7.2 (2008): 271-285. <http://eudml.org/doc/272281>.

@article{Franzén2008,
abstract = {We prove that continuity properties of bounded analytic functions in bounded smoothly bounded pseudoconvex domains in two-dimensional affine space are determined by their behaviour near the Shilov boundary. Namely, if the function has continuous extension to an open subset of the boundary containing the Shilov boundary it extends continuously to the whole boundary. If it is e.g. Hölder continuous on such a boundary set, it is Hölder continuous on the closure of the domain. The statements may fail if the boundary is not smooth.},
author = {Franzén, Salla, Jöricke, Burglind},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {pseudoconvex domain; Shilov boundary; analytic function of several variables; modulus of continuity},
language = {eng},
number = {2},
pages = {271-285},
publisher = {Scuola Normale Superiore, Pisa},
title = {On propagation of boundary continuity of holomorphic functions of several variables},
url = {http://eudml.org/doc/272281},
volume = {7},
year = {2008},
}

TY - JOUR
AU - Franzén, Salla
AU - Jöricke, Burglind
TI - On propagation of boundary continuity of holomorphic functions of several variables
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2008
PB - Scuola Normale Superiore, Pisa
VL - 7
IS - 2
SP - 271
EP - 285
AB - We prove that continuity properties of bounded analytic functions in bounded smoothly bounded pseudoconvex domains in two-dimensional affine space are determined by their behaviour near the Shilov boundary. Namely, if the function has continuous extension to an open subset of the boundary containing the Shilov boundary it extends continuously to the whole boundary. If it is e.g. Hölder continuous on such a boundary set, it is Hölder continuous on the closure of the domain. The statements may fail if the boundary is not smooth.
LA - eng
KW - pseudoconvex domain; Shilov boundary; analytic function of several variables; modulus of continuity
UR - http://eudml.org/doc/272281
ER -

References

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