Glasnik Matematicki, Vol. 57, No. 2 (2022), 313-319. \( \)


Marco Vitturi

School of Mathematical Sciences, University College Cork, Western Gateway Building, Western Road, Cork, Ireland

Abstract.   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.

2020 Mathematics Subject Classification.   42B10, 42B25

Key words and phrases.   Fourier restriction, maximal operators

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