Let X, Y be two complex manifolds of dimension 1 which are countable at infinity, let D ⊂ X, G ⊂ Y be two open sets, let A (resp. B) be a subset of ∂D (resp. ∂G), and let W be the 2-fold cross ((D∪A)×B) ∪ (A×(B∪G)). Suppose in addition that D (resp. G) is Jordan-curve-like on A (resp. B) and that A and B are of positive length. We determine the "envelope of holomorphy" Ŵ of W in the sense that any function locally bounded on W, measurable on A × B, and separately holomorphic on (A × G) ∪ (D × B) "extends" to a function holomorphic on the interior of Ŵ.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap90-2-5,
author = {Peter Pflug and Vi\^et-Anh Nguy\^en},
title = {Boundary cross theorem in dimension 1},
journal = {Annales Polonici Mathematici},
volume = {92},
year = {2007},
pages = {149-192},
zbl = {1122.32006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap90-2-5}
}
Peter Pflug; Viêt-Anh Nguyên. Boundary cross theorem in dimension 1. Annales Polonici Mathematici, Tome 92 (2007) pp. 149-192. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap90-2-5/