Solution with estimates of the \({\bar \partial}\)-equation in analytic polyhedra of general position (Q795972)

For the \({\bar \partial}\)-equation (1) \({\bar \partial}u=f\) where f is a closed (0,r) differential form in \({\mathbb{C}}^ n\) and u is a (0,r-1) differential form, the author proves the following theorem: The \({\bar \partial}\) equation (1) has a solution u in D, an analytic polyhedra in general position, with the estimation \(\sup_{\xi \in D}| u(\xi)| \leq \gamma \sup_{\xi \in D}| f(\xi)|.\)