On Laplace--Carleson embeddings

Dr Eskil Rydhe, University of Leeds. Part of the Analysis and Applications Seminar Series.

The talk is based on a work in progress, and deals with $L^p$ mapping properties of the one-sided Laplace transform. After a brief recollection of previous work by Jacob, Partington and Pott, I present a new result on so-called Laplace--Carleson embeddings.

The main novelty of my result is that it extends beyond the regime of the Hausdorff--Young theorem. I will also discuss a simple connection to a result by Hardy and Littlewood. Given its simplicity, the natural formulation for this talk seems surprisingly difficult to find in the literature.