The Cauchy Transform and Henkin Operator on Convex Domains of Maximal Type F in ℂ 2

Let Ω be a smoothly bounded, convex domain in ℂ2, satisfying the maximal type F. In this paper, we consider the boundary Lipschitz regularity and Gevrey regularity of the Cauchy transform C[u] on Ω, with an application of the Henkin operator for ∂̄-equation. Here, the notion of maximal type F contains all domains of strictly finite type and many cases of infinite type in the sense of Range.