On the Holomorphic Extension of CR Distributions from Non Generic CR Submanifolds of ${\text{C}}^L$

We give a holomorphic extension result from non generic CR submanifold of ${\text{C}}^L$ of positive CR dimension. We consider $N$ a non generic CR submanifold given by $N=\{\text{n},h(\text{n})\}$ where $\text{n}$ is a generic submanifold of some ${\text{C}}^{\mathrm{\ell }}$ and $h$ is a CR map from $\text{n}$ into ${\text{C}}^n$. We prove that if $\text{n}$ is a hypersurface then any CR distribution on $N$ extends holomorphically to a complex transversal wedge, we then generalize this result for arbitrary $\text{n}$ in the case where the graphing function $h$ is decomposable at some $p^{\mathrm{\prime }}\in \text{n}$. We show that any CR distribution on $N$ that is decomposable at $p=(p^{\mathrm{\prime }},h(p^{\mathrm{\prime }}))$ extends holomorphically to a complex transversal wedge.