Let D ⊂ ℂⁿ and 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap84-3-6,
author = {Peter Pflug and Vi\^et-Anh Nguy\^en},
title = {A boundary cross theorem for separately holomorphic functions},
journal = {Annales Polonici Mathematici},
volume = {83},
year = {2004},
pages = {237-271},
zbl = {1068.32010},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap84-3-6}
}
Peter Pflug; Viêt-Anh Nguyên. A boundary cross theorem for separately holomorphic functions. Annales Polonici Mathematici, Tome 83 (2004) pp. 237-271. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap84-3-6/