$$\label{e4.3}
\left [{{\partial} \over {\partial \overline {z_j}}}  
S(f) \right ]_{\Omega}=0.$$

Note then that ${{\partial} \over {\partial \overline {z_j}}} 
S(f)$ is a holomorphic function of $  w$, for $z$ fixed. It vanishes on a totally real generic submanifold of $\C^{n+m}$ and thus it is null where it is defined.

We note that $\ S(f)$ is holomorphic on a set of the form $\B_{3\epsilon} \times \left [\R_+^{n+m} \times i
\Gamma \right ]$ where $R_+^{n+m}=\R^{n+m} \cap \{t_1>0\}$ and $\Gamma \subset
\R^{n+m}$, thus by theorem 2.5.10 in [@[Ho]], we conclude that if $ch\Gamma$ stands for the convex hull of $\Gamma$ then $S(f)$ is holomorphic on $\B_{3\epsilon} \times \left [\R_+^{n+m} \times i ch\Gamma \right
] $.

To conclude the proof of proposition \[Prop1\] we need to show that the holomorphic extension obtained has slow growth and thus its boundary value agrees with our original CR distribution $f$. $S(f)$ is holomorphic in some wedge $\W$ and admits a boundary value when approaching $\n \times \{0\}$ along $\n \times \R^{n} \cap \{t_1>0\}$, hence $S(f)$ has at most slow growth when approaching $\n \times \{0\}$ along $\n \times \R^{n} \cap \{t_1>0\}$. By continuity, it has at most slow growth on any wedge $\W^0 \subset \W$, hence $S(f)$ admits 