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

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.

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This work was supported by the Knut and Alice Wallenberg foundation, scholarship KAW 2016.0442, and produced while the author was a postdoc at University of Leeds, UK.

Received 26 July 2019

Received revised 6 February 2020

Accepted 20 February 2020

Published 3 November 2020