Estimées Ck pour l'équation [formula omitted] sur un convexe de type fini de [formula omitted

Abstract

Let q=1,…, n−1 and D be a bounded convex domain in C n of finite type m. We construct two integral operators T q and T q such that for all p∈ N, T q, T q :C p 0,q(bD)→C p+1/m 0,q−1(bD) are continuous, and for all (0, q)-forms h continuous on bD with ∂ bh continuous on bD too, with the additional hypothesis when q= n−1 that ∫ bD h∧ φ=0 for all φ∈ C ∞ n,0 ( bD) ∂ ̄ b -fermée, we show h= ∂ ̄ b(T q− T q)h+(T q+1− T q+1) ∂ ̄ bh . For this construction, we use the Diederich–Fornæss support function of Alexandre (Publ. IRMA Lille 54 (III) (2001)). To prove the continuity of T q , we integrate by parts and take care of the tangential derivatives. The normal component in z of the kernel of T q will have a bad behaviour, so, in order to find a good representative of its equivalence class, we isolate the tangential component of the kernel and then integrate by parts again. To cite this article: W. Alexandre, C. R. Acad. Sci. Paris, Ser. I 338 (2004).