Let D be a bounded strictly pseudoconvex domain with smooth boundary and f = (f1, ..., fp) (fi ∈ Hol(D)) a complete intersection with normal crossing. In this paper we study an extension problem in L∞-norm for holomorphic functions defined on f-1(0) ∩ D and a decomposition formula g = ∑i=1 p figi for holomorphic functions g ∈ I(f1, ..., fp)(D) in Lipschitz spaces. We stress that for the two problems the classical theorem cannot be applied because f-1(0) has singularities on the boundary ∂D. This work is the first step to understand this type of problem in the general singular case.
@article{urn:eudml:doc:41433,
title = {Extension et division dans les vari\'et\'es \`a croisements normaux.},
journal = {Publicacions Matem\`atiques},
volume = {45},
year = {2001},
pages = {343-369},
mrnumber = {MR1876911},
zbl = {0999.32002},
language = {fr},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41433}
}
Maati, Abderrabi; Mazzilli, Emmanuel. Extension et division dans les variétés à croisements normaux.. Publicacions Matemàtiques, Tome 45 (2001) pp. 343-369. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41433/