Division et extension dans des classes de Carleman de fonctions holomorphes

Let Ω be a bounded pseudoconvex domain in $ℂ^n$ with $C^1$ boundary and let X be a complete intersection submanifold of Ω, defined by holomorphic functions $v_1,...,v_p$ (1 ≤ p ≤ n-1) smooth up to ∂Ω. We give sufficient conditions ensuring that a function f holomorphic in X (resp. in Ω, vanishing on X), and smooth up to the boundary, extends to a function g holomorphic in Ω and belonging to a given strongly non-quasianalytic Carleman class ${l!M_l}$ in $\bar Ω$ (resp. satisfies $f = v_1 f_1+... + v_p f_p$ with $f_1,...,f_p$ holomorphic in Ω and ${l!M_l}$-regular in $\bar Ω$). The essential assumption is that f and $v_1,... ,v_p$ belong to some (maybe smaller) Carleman class ${l!M^-_l}$, where the sequences $M^-$ and M are precisely related by geometric conditions on X and Ω.