Resumen de Extension et division dans les variétés à croisements normaux

Abderrabi Maati, Emmanuel Mazzilli

• Let D be a bounded strictly pseudoconvex domain with smooth boundary and f = (f1, ..., fp) (fi Î Hol(D)) a complete intersection with normal crossing. In this paper we study an extension problem in L8-norm for holomorphic functions defined on f-1(0) n D and a decomposition formula g = ?i=1p figi for holomorphic functions g Î 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.