# Laplace--Carleson embeddings on model spaces and boundedness of truncated Hankel and Toeplitz operators

## TL;DR

This paper characterizes bounded embeddings related to Laplace transform-induced isomorphisms and provides necessary and sufficient conditions for the boundedness of truncated Hankel and Toeplitz operators, including weighted cases.

## Contribution

It introduces new characterizations of bounded embeddings and establishes criteria for the boundedness of truncated Hankel and Toeplitz operators in weighted settings.

## Key findings

- Characterization of bounded embeddings via Laplace--Carleson measures.
- Necessary and sufficient conditions for boundedness of truncated Hankel operators.
- Necessary and sufficient conditions for boundedness of truncated Toeplitz operators.

## Abstract

A characterisation is given of bounded embeddings from weighted $L^2$ spaces on bounded intervals into $L^2$ spaces on the half-plane, induced by isomorphisms given by the Laplace transform onto weighted Hardy and Bergman spaces (Zen spaces). As an application necessary and sufficient conditions are given for the boundedness of truncated Hankel and Toeplitz integral operators, including the weighted case.