L2 estimates and existence theorems for the $\bar \partial $ operator

The theory of analytic function of several complex variables, as presented for example in the Cartan seminars [7], consists in a reduction to the theory of analytic functions of one complex variable.First one only studies functions in polycylinders (products of open sets in the different coordinate planes).The extension of the results to more general domains is then achieved by embedding them as submanifolds of polycylinders in spaces of high dimension.The success of this procedure depends of course on the invariance of