CR-distribution given on a hypersurface (Q1599452)

Let \(\Omega\) be a domain in \(\mathbb{C}^n\), \(n>1\) and let \(\Gamma \subset\Omega\) be a smooth (real) hypersurface \(\Gamma=\{z\in \Omega\mid \rho (z)=0\}\), where \(\rho\in {\mathcal C}^\infty (\Omega)\) is a real valued function. Let \(\Omega^-=\{z \in\Omega\mid \rho(z)<0\}\) and let \(\Omega^+=\Omega \setminus (\Omega^-\cup \Gamma)\). Let \(f\in{\mathcal D}'(\Gamma)\) be a distribution on \(\Gamma\). In this note, the authors give necessary and sufficient conditions for \(f\) to be a CR-distribution. As a corollary, one obtains necessary and sufficient conditions for the holomorphic prolongation of \(f\) in \(\Omega^+\). The proofs are based on the use of Bochner-Martinelli transform.