Laplace-Carleson Embeddings: Completing the picture

Motivated by applications in the control theory of infinite-dimensional systems, several authors have investigated the boundedness of the Laplace transform ℒ: L^p(0, ∞) → L^q(ℂ₊, μ) in terms of properties of the measure μ, with the case q = p = 2 being the classical Carleson Embedding Theorem. We will cover the case p > 2, thus completing the picture to all p, q with 1/p + 1/q ≤ 1. In case p > 2, the Laplace-Carleson Embedding Theorem can also be seen as an appropriate replacement of the Hausdorff-Young inequality.

This is joint work with Eskil Rydhe (Lund).