Publication date: 30 December 2022
Volume: Vol 57
Issue: Svezak 2
Pages: 313-319
DOI: https://doi.org/10.3336/gm.57.2.10
Glasnik matematički, Vol. 57 No. 2, 2022.
Original scientific paper
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
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.
Keywords
Fourier restriction, maximal operators
Hrčak ID:
289610
URI
Publication date:
30.12.2022.
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