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Complex Transversal Holomorphic Extension in Manifolds of type $N=(\n,0)$
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We first consider the case where the graph of $\n$ is trivial, i.e. $h
\equiv 0$.

\[Th2\] Let $N=\{(\n,0)\} $ be a smooth ($\CC^{\infty})$ non generic CR submanifold of $\C^{k+m+n}$. Let $\{v\}$ be complex transversal to $N$ at $p_0$. If $f$ is a CR distribution on $N$ that is decomposable at $p_0$, then there exists a wedge $\W$ of direction $v$ whose edge contains $N$ and $F\in \O(\W_{v})$ such that the boundary value of $F$ on $N$ is $f$.

The main tool to prove theorem \[Th2\] is the following proposition:

\[Prop1\] Let $N=\{(\n,0)\} $ be a smooth ($\CC^{\infty})$ non generic CR submanifold of $\C^{k+m+n}$ and let $f$ be a distribution on $N$ that admits a holomorphic extension to a wedge $\W$ in $\C^{k+m}$ with edge $\n$ near $p_0$, then for any $v$ complex transversal to $N$ at $p_0$, there exists a wedge $\W_v$ in $\C^{k+m+n}$ of direction $v$ whose edge contains $\n$ and $F \in \O(\W_v)$ such that the boundary value of $F$ on $N$ is $f$.

[**Proof of Theorem \[Th2\].**]{} We assume proposition \[Prop1\]. Let $v$ be a complex transversal vector and let $u$ be a CR distribution 