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https://doi.org/10.3336/gm.57.2.10

A note on maximal Fourier restriction for spheres in all dimensions

Marco Vitturi orcid.org/0000-0003-3351-6620 ; School of Mathematical Sciences, University College Cork, Western Gateway Building, Western Road, Cork, Ireland

Preuzmi JATS datoteku

Sažetak

We prove a maximal Fourier restriction theorem for hypersurfaces in \(\mathbb{R}^{d}\) for any dimension \(d\geq 3\) in a restricted range of exponents given by the Tomas-Stein theorem (spheres being the most canonical example). The proof consists of a simple observation. When \(d=3\) the range corresponds exactly to the full Tomas-Stein one, but is otherwise a proper subset when \(d>3\). We also present an application regarding the Lebesgue points of functions in \(\mathcal{F}(L^p)\) when \(p\) is sufficiently close to 1.

Ključne riječi

Fourier restriction, maximal operators

Hrčak ID:

289610

URI

https://hrcak.srce.hr/289610

Datum izdavanja:

30.12.2022.

Posjeta: 689 *