Revistes Catalanes amb Accés Obert (RACO)

Extension et division dans les variétés à croisements normaux

A. Maati, E. Mazzilli

Resum


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.

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