Holomorphic extension of decomposable distributions from a CR submanifold of \(\mathbb C^L\) (Q874444)

In this paper wedge extendability of CR distributions defined on non generic CR submanifolds \(M\) of \(\mathbb{C}^L\) is investigated. Such an \(M\) can be obtained as a graph of a CR map \(h:N\to\mathbb{C}^n\), for some generically embedded \(N\subset\mathbb{C}^{k+m}\), of the same CR dimension \(k\) of \(M\). The main result is that, in case the function \(h\) is wedge-decomposable, each CR distribution \(f\) on \(M\) that is wedge-decomposable is also the boundary value of a holomorphic function \(F\) defined in a wedge pointing in a complex direction \(v\) transversal to \(M\).