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

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.