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Maximal restriction estimates and the maximal function of the Fourier transform


Author: João P. G. Ramos
Journal: Proc. Amer. Math. Soc. 148 (2020), 1131-1138
MSC (2010): Primary 42B10, 42B25, 42B37
DOI: https://doi.org/10.1090/proc/14805
Published electronically: November 6, 2019
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Abstract: We prove inequalities concerning the restriction of the strong maximal function of the Fourier transform to the circle, providing an answer to a question left open by Müller, Ricci, and Wright. We employ methods similar in spirit to the classical proofs of the two-dimensional restriction theorem, with the addition of a suitable trick to help us linearise our maximal function. In the end, we comment on how to use the same linearisation trick in combination with Vitturi's duality argument to obtain sharper high-dimensional results for the Hardy-Littlewood maximal function.


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Additional Information

João P. G. Ramos
Affiliation: Mathematisches Institut, Universität Bonn, D - 53115 Bonn, Germany

DOI: https://doi.org/10.1090/proc/14805
Keywords: Maximal functions, Fourier restriction, Fourier transform
Received by editor(s): November 1, 2018
Received by editor(s) in revised form: April 25, 2019, and June 30, 2019
Published electronically: November 6, 2019
Communicated by: Svitlana Mayboroda
Article copyright: © Copyright 2019 American Mathematical Society