Holder estimates for partial d-bar in two-dimensional complex euclidean space
Jay Belanger · 1987
This paper is a further investigation into integral kernels for solving $\bar\partial$ on weakly pseudoconvex domains in $\doubc$ started by J. E. Fornaess in (2). In that paper, he constructed a kernel for solving $\bar\partial$ on Kohn-Nirenberg domains, and showed that the solutions obtained satisfied sup-norm estimates. In this paper, a kernel for solving $\bar\partial$ is constructed on a larger class of domains, and using this kernel it is shown that the solutions obtained satisfy Holder estimates.