---
author:
- 'Nicolas Eisen  eisen@math.univ-poitiers.fr'
title: 'ON THE HOLOMORPHIC EXTENSION OF CR DISTRIBUTIONS FROM NON GENERIC CR SUBMANIFOLDS OF $\C^L$'
---

Introduction
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Statement of Results
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Let $\n$ be a smooth generic submanifold of $\C^{k+m}$ of CR dimension $k$ and $h$ a smooth CR map from $\n$ into some $\C^{n}$ verifying $dh(0)=0$. Set $L=k+m+n$, we construct a CR submanifold $N$ of $\C^{p}$ near the origin as the graph of $h$ over $\n$, that is $N=\{(\n,h(\n))\}$. It turns out that any non generic CR submanifold of $\C^L$ can be obtained in that fashion, see for example [@[Bo]]. The main question we address in this paper is the possible holomorphic extension of CR functions of $N$ to some wedge $\W$ in a complex transverse direction. We say that a vector in $\C^L$ is [**complex transversal**]{} to $N$ at $p \in N$ if $v \not \in $ span$_{\C}T_pN$. For totally real submanifolds of $\C^L$, we have the following well known result (see the remarks following for different proofs of this result). If $N$ is a non generic totally real submanifold of $\C^L$ and $ v \in \C^L$ is complex transversal to $N$ at $p$. Then for any continuous function $f$ on 