Let D be a bounded strictly pseudoconvex domain with smooth boundary and f = (f 1 ,. .. , fp) (f i ∈ 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 = p i=1 f i g i for holomorphic functions g ∈ I (f 1 ,...,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.

The goal of this work is to prove that locally in R: 1. every rigid Cauchy-Riemann structure V beloging to a Holder class of a noninteger e.rponent is realizable by a díffeomorphism beloging to another Holder class whose ímage *(V) ís the standanl comple1: structure of a rigid hypersurf'ace in C 2 ' obtened by a restnction of thc .fields a~) Z¡ anda~) of C w T(C 2).

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