Extension et division dans les variétés à croisements normaux

Let $D$ be a bounded strictly pseudoconvex domain with smooth boundary and $f=(f_1,\dotsc, f_p)$ ($f_i\in\operatorname{Hol}(\bar D)$) a complete intersection with normal crossing. In this paper we study an extension problem in $L^{\infty}$-norm for holomorphic functions defined on $f^{-1}(0)\cap D$...

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Bibliographic Details
Published in:Publicacions matemàtiques 2001, Vol.45 (2), p.343-369
Main Authors: Maati, A., Mazzilli, E.
Format: Article
Language:eng ; fre
Subjects:
Dominios pseudoconvexos
Espacio de Lipschitz
Funciones holomorfas
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Summary:Let $D$ be a bounded strictly pseudoconvex domain with smooth boundary and $f=(f_1,\dotsc, f_p)$ ($f_i\in\operatorname{Hol}(\bar D)$) a complete intersection with normal crossing. In this paper we study an extension problem in $L^{\infty}$-norm for holomorphic functions defined on $f^{-1}(0)\cap D$ and a decomposition formula $g=\sum_{i=1}^{p}f_ig_i$ for holomorphic functions $g\in I_{(f_1,\dotsc,f_p)}(D)$ 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 $\partial D$. This work is the first step to understand this type of problem in the general singular case.
ISSN:0214-1493
2014-4350
DOI:10.5565/PUBLMAT_45201_03