# A boundary cross theorem for separately holomorphic functions

Annales Polonici Mathematici (2004)

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

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topPeter 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 -

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