a boundary value on $\n \times \{0\}$, which by uniqueness of boundary value is $f$. This concludes the proof of proposition \[Prop1\]. $\blacksquare$

Proof of the Main Results and Remarks
=====================================

Proof of the Results on Decomposable CR Distributions
-----------------------------------------------------

[**Proof of Theorem \[t1\].**]{} Recall that $  N=\{(  \n,h(  \n))\}$. Consider the CR map $h: 
\n \to \C^n$. By theorem \[Th2\], each $h_j$ extends holomorphically to some wedge $\W_j$. Set $\W =\cap_{j=1}^n \W_j$. Define $F:(  \n,0) \to (\n,\kappa h(  \n))$ where $\kappa \in \R^*$ by $$F(z,w',w'')=(z,w',w''+\kappa h(z,w')).$$ Clearly, there exists $\kappa\not = 0$ so that on $\overline \W$, the Jacobian of $F$ is non zero, without loss of generality, we can assume that $\kappa=1$. Hence $F$ is a biholomorphism from $\W$ to $F(\W)$ extending smoothly to a diffeomorphism from $\overline \W$ to $F(\overline \W)$. Since $dh(0)=0$, $F$ is tangent to the identity at the origin, hence there exists $\W'$ a wedge of direction $v$ such that $\W'\subset F(\W)$. We then conclude that any decomposable CR distribution on $N$ extends holomorphically to a complex transversal wedge of direction $v$.

To prove (B), we note that $f_j=w''_j-h_j$ are holomorphic in $\W$ and, since $dh_j(0)=0$, we conclude that $$d(w''_1-h_1)\wedge...\wedge d(w''_n-h_n)\not =0~~{\rm on} \W.$$ 