A boundary cross theorem for separately holomorphic functions

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 -