Necessary conditions for Hölder regularity gain of d-bar equation in C^3

Abstract

Suppose that a smooth holomorphic curve $V$ has order of contact $\eta$ at a point $w_0$ in the boundary of a pseudoconvex domain $\Omega$ in ${\mathbb{C}}^3.$ We show that the maximal gain in Hölder regularity for solutions of the $\bar{\partial }$-equation is at most $\frac{1}{\eta }.$