# Composition operators on the spaces of Harmonic Bloch functions

## TL;DR

This paper investigates the properties of composition operators on harmonic Bloch function spaces, providing criteria for boundedness, compactness, and estimates of their essential norms, extending known results from classical Bloch spaces.

## Contribution

It introduces new characterizations of boundedness and compactness for composition operators on harmonic Bloch spaces and estimates their essential norms, expanding existing literature.

## Key findings

- Provided equivalent conditions for boundedness and compactness.
- Estimated the essential norm of composition operators.
- Extended results from classical Bloch spaces to harmonic Bloch functions.

## Abstract

In this paper we characterize some basic properties of composition operators on the spaces of harmonic Bloch functions. First we provide some equivalent conditions for boundedness and compactness of composition operators. Then by using these conditions we estimate the essential norm of composition operators. These results extends the similar results that were proven in the literature on the Bloch spaces.