of $\C^L$ containing through some $p_0 \in M$ a proper smooth ($\CC^{\infty}$) CR submanifold $N=(\n,h(\n))$ of same CR dimension, write $p_0=(p'_0,h(p'_0))$ with $p'_0\in \n$. Assume that the function $h$ decomposable at $p'_0$. Let $v\in T_{p_0}M \setminus 
\left [span_{\C}T_{p_0}N\right ]$. If $f$ is a decomposable CR distribution at $p_0$, then there exists a wedge $\W$ in $M$ of direction $v$ whose edge contains $N$ and $F$ smooth ($\CC^{\infty}$) CR functions on $\W$ such that the boundary value of $F$ on $N$ is $f$. Furthermore, there exists a collection of smooth CR functions $\{g_{\l}\}_{\l=1}^n$ vanishing to order one on $N$ and such that $dg_1\wedge....\wedge
dg_n \not=0 $ on $\W$.

Remarks
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The equivalent of theorem \[th\] for totally real manifolds (mentioned in the introduction) can be proved in several ways, one way is to follow the theory of analytic vectors of an elliptic operator due to Treves (see section 3.2). Another way is to use the following result: Let $N$ be a smooth submanifold of the boundary of $\Omega$, a strictly pseudoconvex domain in $\C^L$. If $N$ is complex tangential ($TN
\subset (T(\partial \Omega) \cap iT(\partial \Omega))$) then $N$ is a Pic interpolating set. See for example [@[Na]] or [@[Ru]]. Given $N$, 