Ck-regularity for ∂¯-equations for a class of convex domains of infinite type in C2

Abstract

The main purpose of this article is to study $C^k$-regularity ($k=0,1,\dots$) for the Cauchy–Riemann equation $$\overline{\partial }u=\varphi$$ on a smoothly bounded, convex domain of infinite type in ${\mathbb{C}}^2$.