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October 2020 On Laplace–Carleson embeddings, and $L^p$-mapping properties of the Fourier transform
Eskil Rydhe
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Ark. Mat. 58(2): 437-457 (October 2020). DOI: 10.4310/ARKIV.2020.v58.n2.a10

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.

Funding Statement

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.

Citation

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Eskil Rydhe. "On Laplace–Carleson embeddings, and $L^p$-mapping properties of the Fourier transform." Ark. Mat. 58 (2) 437 - 457, October 2020. https://doi.org/10.4310/ARKIV.2020.v58.n2.a10

Information

Received: 26 July 2019; Revised: 6 February 2020; Published: October 2020
First available in Project Euclid: 16 January 2021

Digital Object Identifier: 10.4310/ARKIV.2020.v58.n2.a10

Rights: Copyright © 2020 Institut Mittag-Leffler

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Vol.58 • No. 2 • October 2020
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