Maximal restriction estimates and the maximal function of the Fourier transform

2018/10/16 by Ramos, João P. G.
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1810.06971

Abstract

We prove a maximal restriction inequality for the Fourier transform, providing an answer to a question left open by Müller, Ricci and Wright. Our methods are similar to the ones in their article, 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 trick in combination with Vitturi's approach to obtain a stronger high-dimensional result.

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