# A boundary cross theorem for separately holomorphic functions

• Volume: 84, Issue: 3, page 237-271
• ISSN: 0066-2216

top

## Abstract

top
Let D ⊂ ℂⁿ and $G\subset {ℂ}^{m}$ be pseudoconvex domains, let A (resp. B) be an open subset of the boundary ∂D (resp. ∂G) and let X be the 2-fold cross ((D∪A)×B)∪(A×(B∪G)). Suppose in addition that the domain D (resp. G) is locally ² smooth on A (resp. B). We shall determine the “envelope of holomorphy” X̂ of X in the sense that any function continuous on X and separately holomorphic on (A×G)∪(D×B) extends to a function continuous on X̂ and holomorphic on the interior of X̂. A generalization of this result to N-fold crosses is also given.

## How to cite

top

Peter Pflug, and Viêt-Anh Nguyên. "A boundary cross theorem for separately holomorphic functions." Annales Polonici Mathematici 84.3 (2004): 237-271. <http://eudml.org/doc/280599>.

@article{PeterPflug2004,
abstract = {Let D ⊂ ℂⁿ and $G ⊂ ℂ^m$ be pseudoconvex domains, let A (resp. B) be an open subset of the boundary ∂D (resp. ∂G) and let X be the 2-fold cross ((D∪A)×B)∪(A×(B∪G)). Suppose in addition that the domain D (resp. G) is locally ² smooth on A (resp. B). We shall determine the “envelope of holomorphy” X̂ of X in the sense that any function continuous on X and separately holomorphic on (A×G)∪(D×B) extends to a function continuous on X̂ and holomorphic on the interior of X̂. A generalization of this result to N-fold crosses is also given.},
author = {Peter Pflug, Viêt-Anh Nguyên},
journal = {Annales Polonici Mathematici},
keywords = {N-fold cross; holomorphic extension; harmonic measure; estimates for plurisubharmonic measures; envelope of holomorphy; separate holomorphicity; Poisson kernels},
language = {eng},
number = {3},
pages = {237-271},
title = {A boundary cross theorem for separately holomorphic functions},
url = {http://eudml.org/doc/280599},
volume = {84},
year = {2004},
}

TY - JOUR
AU - Peter Pflug
AU - Viêt-Anh Nguyên
TI - A boundary cross theorem for separately holomorphic functions
JO - Annales Polonici Mathematici
PY - 2004
VL - 84
IS - 3
SP - 237
EP - 271
AB - Let D ⊂ ℂⁿ and $G ⊂ ℂ^m$ be pseudoconvex domains, let A (resp. B) be an open subset of the boundary ∂D (resp. ∂G) and let X be the 2-fold cross ((D∪A)×B)∪(A×(B∪G)). Suppose in addition that the domain D (resp. G) is locally ² smooth on A (resp. B). We shall determine the “envelope of holomorphy” X̂ of X in the sense that any function continuous on X and separately holomorphic on (A×G)∪(D×B) extends to a function continuous on X̂ and holomorphic on the interior of X̂. A generalization of this result to N-fold crosses is also given.
LA - eng
KW - N-fold cross; holomorphic extension; harmonic measure; estimates for plurisubharmonic measures; envelope of holomorphy; separate holomorphicity; Poisson kernels
UR - http://eudml.org/doc/280599
ER -

## NotesEmbed?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.