On supnorm estimates for $\bar{\partial }$ on infinite type convex domains in ${\mathbb{C}}^2$

Abstract

In this paper, we study the $\bar{\partial }$-equation on some convex domains of infinite type in ${\mathbb{C}}^2$. In detail, we prove that supnorm estimates hold for infinite exponential type domains provided the exponent is less than 1.

15 pages. submitted to J. Geom. Anal