Optimal Hölder regularity for the $\bar{\partial }$ problem on product domains in ${\mathbb{C}}^2$

Abstract

The note concerns the $\bar{\partial }$ problem on product domains in ${\mathbb{C}}^2$. We show that there exists a bounded solution operator from $C^{k,\alpha }$ into itself, $k\in {\mathbb{Z}}^{+}\cup \{0\},0<\alpha <1$. The regularity result is optimal in view of an example of Stein-Kerzman.

References in corpus (1)

• Supnorm estimates for $\bar{\partial }$ on product domains in ${\mathbb{C}}^n$