# Weighted composition operators acting from the Lipschitz space to the space of bounded functions on a tree

## TL;DR

This paper investigates weighted composition operators from Lipschitz spaces to bounded functions on infinite trees, providing characterizations of their boundedness, compactness, isometric properties, and boundedness from below.

## Contribution

It offers a comprehensive analysis of weighted composition operators on trees, including new characterizations of their key properties in this setting.

## Key findings

- Characterized boundedness and compactness of operators
- Determined conditions for isometric operators
- Identified criteria for boundedness from below

## Abstract

We study the weighted composition operators between the Lipschitz space and the space of bounded functions on the set of vertices of an infinite tree. We characterized the boundedness, the compactness, and the boundedness from below of weighted composition operators. We also determine the isometric weighted composition operators.