# 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

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topFranzén, 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 -

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