# Bounded composition operator on Lorentz spaces

## TL;DR

This paper investigates the conditions under which a measurable mapping induces a bounded composition operator on Lorentz spaces, providing necessary and sufficient criteria for boundedness.

## Contribution

It offers a complete characterization of bounded composition operators on Lorentz spaces, which was previously not fully understood.

## Key findings

- Established necessary and sufficient conditions for boundedness
- Characterized the measurable mappings inducing bounded operators
- Enhanced understanding of operator behavior on Lorentz spaces

## Abstract

We study a composition operator on Lorentz spaces. In particular we provide necessary and sufficient conditions under which a measurable mapping induces a bounded composition operator.