# On Laplace--Carleson embeddings, and $L^p$-mapping properties of the Fourier transform

## TL;DR

This paper explores advanced embedding theorems related to Laplace--Carleson operators, extends existing results, and examines Fourier transform properties across various function spaces, contributing new insights into harmonic analysis.

## Contribution

It extends previous results on Laplace--Carleson embeddings for large exponents and discusses Fourier transform mapping properties in Sobolev and Besov spaces.

## Key findings

- Extended results on Laplace--Carleson embeddings for large exponents
- Analyzed Fourier transform mapping properties in Sobolev and Besov spaces
- Provided an example related to an open problem in the field

## Abstract

We investigate so-called Laplace--Carleson embeddings for large exponents. In particular, we extend some results by Jacob, Partington, and Pott. We also discuss some related results for Sobolev- and Besov spaces, and mapping properties of the Fourier transform. These variants of the Hausdorff--Young theorem appear difficult to find in the literature. We conclude the paper with an example related to an open problem.