Composition operators on Bloch and Hardy type spaces

TL;DR

This paper investigates composition operators on Bloch and Hardy type spaces, providing sharp Lipschitz estimates for harmonic functions and extending existing results in the field.

Contribution

It establishes a sharp Lipschitz estimate for harmonic functions in Bloch spaces and explores new classes of composition operators, advancing understanding of their properties.

Findings

Sharp Lipschitz estimate for harmonic functions in Bloch spaces

New classes of composition operators characterized

Results extend and improve previous findings

Abstract

The main purpose of this paper is to discuss Hardy type spaces, Bloch type spaces and the composition operators of complex-valued harmonic functions. We first establish a sharp estimate of the Lipschitz continuity of complex-valued harmonic functions in Bloch type spaces with respect to the pseudo-hyperbolic metric, which gives an answer to an open problem. Then some classes of composition operators on Bloch and Hardy type spaces will be investigated. The obtained results improve and extend some corresponding known results.