Closure of Hardy spaces in the Bloch space

TL;DR

This paper characterizes which Bloch functions can be approximated by Hardy space functions in the Bloch norm, providing new results especially for the case when 0<p≤1, even in the unit disk.

Contribution

It offers a new description of Bloch functions approximable by Hardy space functions, extending known results to the case 0<p≤1.

Findings

Characterization of Bloch functions approximable by Hardy space functions

New results for the case 0<p≤1 in the unit disk

Extension of approximation theory in complex analysis

Abstract

A description of the Bloch functions that can be approximated in the Bloch norm by functions in the Hardy space $H^p$ of the unit ball of $\Cn$ for $0<p<\infty$ is given. When $0<p\leq1$, the result is new even in the case of the unit disk.