The norm of the backward shift on $H^1$ is $\frac{2}{\sqrt{3}}$

TL;DR

This paper determines the exact norm of the backward shift operator on the Hardy space H^1 as 2/√3 and characterizes the functions where this norm is achieved.

Contribution

It provides the precise value of the backward shift's norm on H^1 and identifies the extremal functions for this operator.

Findings

The norm of the backward shift on H^1 is 2/√3.

Functions attaining the norm are explicitly characterized.

Abstract

We show that the norm of the backward shift operator on $H^1$ is $2/\sqrt{3}$, and we identify the functions for which the norm is attained.