a totally real non generic submanifold of $\C^L$, one can easily construct $\Omega$ as above and deduce the theorem.

The boundary value of a holomorphic function is well defined for functions of slow growth, that is there exists a constant $C>0$ and a positive integer $\ell$ such that $|F(z)|\leq {{C}\over{|dist(z,N)|^{\ell}}},$ where $dist(z,M)$ denotes the distance from a point $z$ to $N$. Conversely any CR distribution which extends holomorphically to a wedge $\W$ is given by the boundary value of a holomorphic function of slow growth. See for example [@[BER]].

As it is noted in [@[Tr-3]] on most CR submanifolds of $\C^L$ all CR functions are decomposable, hence the hypotheses of theorem \[t1\] hold in a generical sense. However, they are examples of CR submanifolds of $\C^L$ on which indecomposable CR functions exist, see [@[Tr-3]] for the general theory and [@[Rosay]] for an elementary explanation of such examples. It turns out that on Trépreau’s original example of a CR manifold where undecomposable CR functions exist we still do get holomorphic extension of CR functions to complex transversal wedges (see section 3.2).

Theorem \[t1\] implies that the extension obtained is not unique, which differs greatly with the holomorphic extension results obtained for 