Characterizations of composition operators on Bloch and Hardy type spaces

TL;DR

This paper characterizes composition operators on Bloch and Hardy type spaces, extending existing results by exploring their properties between various harmonic and pluriharmonic function spaces on the unit disk and ball.

Contribution

It introduces new methods to analyze composition operators between harmonic and pluriharmonic spaces, providing improved characterizations of boundedness and compactness.

Findings

Characterizations of composition operators between harmonic Bloch and pluriharmonic Hardy spaces.

New criteria for boundedness and compactness of composition operators on Lipschitz type spaces.

Extensions of known results to more general settings with doubling weights.

Abstract

The main purpose of this paper is to investigate characterizations of composition operators on Bloch and Hardy type spaces. Initially, we use general doubling weights to study the composition operators from harmonic Bloch type spaces on the unit disc $\mathbb{D}$ to pluriharmonic Hardy spaces on the Euclidean unit ball $\mathbb{B}^n$. Furthermore, we develop some new methods to study the composition operators from harmonic Bloch type spaces on $\mathbb{D}$ to pluriharmonic Bloch type spaces on $\mathbb{D}$. Additionally, some application to new characterizations of the composition operators between pluriharmonic Lipschitz type spaces to be bounded or compact will be presented. The obtained results of this paper provide the improvements and extensions of the corresponding known results.