On Sharp Hölder Estimates of the Cauchy-Riemann Equation on Pseudoconvex Domains in Cn with One Degenerate Eigenvalue

Abstract

Let $\Omega$ be a smoothly bounded pseudoconvex domain in ${\mathbb{C}}^n$ with one degenerate eigenvalue and assume that there is a smooth holomorphic curve $V$ whose order of contact with $b\Omega$ at $z_0\in b\Omega$ is larger than or equal to $\eta$. We show that the maximal gain in Hölder regularity for solutions of the $\overline{\partial }$-equation is at most $1/\eta$.