Hypercyclic and mixing composition operators on $H^{p}$

TL;DR

This paper characterizes when composition operators induced by automorphisms of the unit disk are hypercyclic or mixing on Hardy spaces $H^p$, extending prior results to all $p$ in the range.

Contribution

It provides a complete characterization of hypercyclic and mixing composition operators on $H^p$ spaces for all $p$ between 1 and infinity, generalizing earlier work.

Findings

Characterization of hypercyclic composition operators on $H^p$

Characterization of mixing composition operators on $H^p$

Extension of previous results to all $p$ in [1, ∞)

Abstract

Extending previous results of Bourdon and Shapiro we characterize the hypercyclic and mixing composition operators $C_{\varphi}$ for the automorphisms of $\mathbb{D}$ on any of the spaces $H^{p}$ with $1\leqslant p<+\infty$.