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.