Green form to intrinsic metric of a ball (Q1120706)

The author gives an alternative proof for a solution of the \(\partial\)- Neumann problem with respect to the open unit ball \[ B^ n:=\{(z_ 1,z_ 2,...,z_ n)\in {\mathbb{C}}^ n:\quad \sum^{n}_{j=1}| z_ j|^ 2<1\}, \] \(n\geq 2\), differentiable (0,1)-form g with compact support. He explicitely constructs an appropriate Green form N(z,w), which vanishes on the boundary \(\partial B^ n\). Then he shows, that one can apply Kohn's standard program [see \textit{J. J. Kohn}, Proc. Symp. Pure Math. 41, 137-145 (1982; Zbl 0535.32010)] to get his main Theorem 2. Let g be a differentiable (0,1)-form with compact support in \(B^ n\) and \({\bar \partial}g=0\). Then \[ v(w):={\bar \partial}^*\int_{B^ n}g(z)\wedge *_ z\overline{N(z,w)} \] is a solution of the \({\bar \partial}\)-equation \({\bar \partial}v=g\) and v vanishes on the boundary \(\partial B^ n\).