%0 Journal Article %T On supnorm estimates for $\bar\partial$ on infinite type convex domains in $\mathbb C^2$ %A John Erik Fornaess %A Lina Lee %A Yuan Zhang %J Mathematics %D 2009 %I arXiv %X 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. %U http://arxiv.org/abs/0911.2277v1