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arXiv · 1810.06971

Maximal restriction estimates and the maximal function of the Fourier transform

João P. G. Ramos
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Abstract

We prove a maximal restriction inequality for the Fourier transform, providing an answer to a question left open by M\"uller, 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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João P. G. Ramos. 2018-10-16. Maximal restriction estimates and the maximal function of the Fourier transform. https://arxiv.org/abs/1810.06971

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