Hardy spaces of holomorphic functions for domains in $\mathbb C^n$ with minimal smoothness

TL;DR

This paper investigates Hardy spaces of holomorphic functions on certain bounded domains in complex n-space with minimal boundary smoothness, establishing key representations and density results under convexity conditions.

Contribution

It provides new representation and density theorems for Hardy spaces on domains with minimal boundary regularity in complex spaces.

Findings

Established representation formulas for Hardy spaces on $C^2$ and $C^{1,1}$ domains.

Proved density of smooth functions in Hardy spaces under minimal boundary regularity.

Extended Hardy space theory to domains with minimal smoothness and convexity conditions.

Abstract

We prove various representations and density results for Hardy spaces of holomorphic functions for two classes of bounded domains in $\mathbb C^n$, whose boundaries satisfy minimal regularity conditions (namely the classes $C^2$ and $C^{1,1}$ respectively) together with naturally occurring notions of convexity.