Laplace-Carleson embeddings and infinity-norm admissibility

TL;DR

This paper characterizes the boundedness of Laplace--Carleson embeddings on $L^ Infty$ and Orlicz spaces, linking it to Carleson intensity and Berezin transforms, with applications to control operator admissibility.

Contribution

It provides a full characterization of boundedness conditions for Laplace--Carleson embeddings on $L^ Infty$ and Orlicz spaces, advancing control theory applications.

Findings

Characterization of boundedness of Laplace--Carleson embeddings on $L^ Infty$

Results on boundedness for a large class of Orlicz spaces

Applications to admissibility of control operators in linear systems

Abstract

A full characterization of the boundedness of Laplace--Carleson embeddings on $L^\infty$ is provided, in terms of the Carleson intensity of the respective measure and of a suitable weighted Berezin transform of the measure. Moreover, boundedness results, and in some cases full characterizations of boundedness, are proved for a large class of Orlicz spaces. These findings are crucial for characterizing admissibility of control operators for linear diagonal semigroup systems in a variety of contexts. A particular focus is laid on essentially bounded inputs.