Necessary conditions for H\"older 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 H\"older regularity for solutions of the $\bar{\partial}$-equation is at most $\frac{1}{\eta}.$