An approximation theorem for Hardy functions on $\mathbb {C}$-linearly convex domains of infinite type in $\mathbb {C}^2$

Abstract

Let $\Omega \subset \mathbb {C}^2$ be a smoothly bounded, $\mathbb {C}$-linearly convex domain. We prove that if $\Omega $ is of $F$-type at all boundary points (for some type function $F$), then for all $1\le p \lt \infty $, every Hardy function $f\in H^