The Stein–Tomas inequality under the effect of symmetries

Rainer Mandel; Diogo Oliveira e silva

doi:10.1007/s11854-023-0282-3

The Stein–Tomas inequality under the effect of symmetries

Rainer Mandel, Diogo Oliveira e silva^*

^*Corresponding author for this work

Mathematics

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Abstract

We prove new Fourier restriction estimates to the unit sphere Sd−1 on the class of O(d − k) × O(k)-symmetric functions, for every d ≥ 4 and 2 ≤ k ≤ d − 2. As an application, we establish the existence of maximizers for the endpoint Stein–Tomas inequality within that class. Moreover, we construct examples showing that the range of Lebesgue exponents in our estimates is sharp.

Original language	English
Pages (from-to)	547-582
Journal	Journal d'Analyse Mathématique
Volume	150
Issue number	2
Early online date	20 Jun 2023
DOIs	https://doi.org/10.1007/s11854-023-0282-3
Publication status	Published - 1 Sept 2023

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https://link.springer.com/10.1007/s11854-023-0282-3

Sharp Fourier Restriction Theory
Oliveira E Silva, D.
Engineering & Physical Science Research Council
1/02/20 → 31/01/22
Project: Research Councils

Cite this

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title = "The Stein–Tomas inequality under the effect of symmetries",

abstract = "We prove new Fourier restriction estimates to the unit sphere Sd−1 on the class of O(d − k) × O(k)-symmetric functions, for every d ≥ 4 and 2 ≤ k ≤ d − 2. As an application, we establish the existence of maximizers for the endpoint Stein–Tomas inequality within that class. Moreover, we construct examples showing that the range of Lebesgue exponents in our estimates is sharp.",

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AB - We prove new Fourier restriction estimates to the unit sphere Sd−1 on the class of O(d − k) × O(k)-symmetric functions, for every d ≥ 4 and 2 ≤ k ≤ d − 2. As an application, we establish the existence of maximizers for the endpoint Stein–Tomas inequality within that class. Moreover, we construct examples showing that the range of Lebesgue exponents in our estimates is sharp.

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M3 - Article

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JO - Journal d'Analyse Mathématique

JF - Journal d'Analyse Mathématique

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The Stein–Tomas inequality under the effect of symmetries

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Sharp Fourier Restriction Theory

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