Sharp Fourier extension for functions with localized support on the circle

Lars Becker

doi:10.4171/RMI/1532

Sharp Fourier extension for functions with localized support on the circle

Lars Becker

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

A well-known conjecture states that constant functions are extremizers of the L² → L⁶ Tomas–Stein extension inequality for the circle. We prove that functions supported in a√6/80-neighborhood of a pair of antipodal points on S¹ satisfy the conjectured sharp inequality. In the process, we make progress on a program formulated by Carneiro, Foschi, Oliveira e Silva and Thiele to prove the sharp inequality for all functions.

Original language	English (US)
Pages (from-to)	2145-2166
Number of pages	22
Journal	Revista Matematica Iberoamericana
Volume	41
Issue number	6
DOIs	https://doi.org/10.4171/RMI/1532
State	Published - Sep 22 2025
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

42B10
Fourier restriction
circle
sharp inequalities

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10.4171/RMI/1532

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title = "Sharp Fourier extension for functions with localized support on the circle",

abstract = "A well-known conjecture states that constant functions are extremizers of the L2 → L6 Tomas–Stein extension inequality for the circle. We prove that functions supported in a√6/80-neighborhood of a pair of antipodal points on S1 satisfy the conjectured sharp inequality. In the process, we make progress on a program formulated by Carneiro, Foschi, Oliveira e Silva and Thiele to prove the sharp inequality for all functions.",

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author = "Lars Becker",

note = "Publisher Copyright: {\textcopyright} 2024 Real Sociedad Matem{\'a}tica Espa{\~n}ola Published by EMS Press and licensed under a CC BY 4.0 license https://creativecommons.org/licenses/by/4.0/",

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N2 - A well-known conjecture states that constant functions are extremizers of the L2 → L6 Tomas–Stein extension inequality for the circle. We prove that functions supported in a√6/80-neighborhood of a pair of antipodal points on S1 satisfy the conjectured sharp inequality. In the process, we make progress on a program formulated by Carneiro, Foschi, Oliveira e Silva and Thiele to prove the sharp inequality for all functions.

AB - A well-known conjecture states that constant functions are extremizers of the L2 → L6 Tomas–Stein extension inequality for the circle. We prove that functions supported in a√6/80-neighborhood of a pair of antipodal points on S1 satisfy the conjectured sharp inequality. In the process, we make progress on a program formulated by Carneiro, Foschi, Oliveira e Silva and Thiele to prove the sharp inequality for all functions.

KW - 42B10

KW - Fourier restriction

KW - circle

KW - sharp inequalities

UR - https://www.scopus.com/pages/publications/105022932083

UR - https://www.scopus.com/pages/publications/105022932083#tab=citedBy

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EP - 2166

JO - Revista Matematica Iberoamericana

JF - Revista Matematica Iberoamericana

IS - 6

ER -

Sharp Fourier extension for functions with localized support on the circle

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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