Integral kernels and Hölder estimates for \({\bar \partial}\) on pseudoconvex domains of finite type in \({\mathbb{C}}^ 2\) (Q757654)

As is well-known, in the strongly pseudoconvex case, by Grauert-Lieb, and independently by Henkin, by using the integral method, the solution for the \({\bar \partial}\)-equation is explicitly obtained and several estimates are shown for this solution. However, in the weakly pseudoconvex case, only for special cases, corresponding results are obtained. The author treats pseudoconvex domains of finite type in \({\mathbb{C}}^ 2\) and obtains an explicit solution and a suitable estimate for this solution.