Extremizers for Fourier restriction inequalities: Convex arcs

Diogo Oliveira E Silva

doi:10.1007/s11854-014-0035-4

Extremizers for Fourier restriction inequalities: Convex arcs

Diogo Oliveira E Silva

Mathematics

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

7 Citations (Scopus)

Abstract

We establish the existence of extremizers for a Fourier restriction inequality on planar convex arcs without points with collinear tangents whose curvature satisfies a natural assumption. More generally, we prove that any extremizing sequence of nonnegative functions has a subsequence which converges to an extremizer.

Original language	English
Pages (from-to)	337-385
Number of pages	49
Journal	Journal d'Analyse Mathématique
Volume	124
DOIs	https://doi.org/10.1007/s11854-014-0035-4
Publication status	Published - Oct 2014

Keywords

Nonnegative Function
Decomposition Algorithm
Projection Measure
Optimal Constant
Disjoint Support

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https://doi.org/10.1007/s11854-014-0035-4Licence: None: All rights reserved

Cite this

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title = "Extremizers for Fourier restriction inequalities: Convex arcs",

abstract = "We establish the existence of extremizers for a Fourier restriction inequality on planar convex arcs without points with collinear tangents whose curvature satisfies a natural assumption. More generally, we prove that any extremizing sequence of nonnegative functions has a subsequence which converges to an extremizer.",

keywords = "Nonnegative Function, Decomposition Algorithm, Projection Measure, Optimal Constant, Disjoint Support",

author = "\{Oliveira E Silva\}, Diogo",

year = "2014",

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T1 - Extremizers for Fourier restriction inequalities

T2 - Convex arcs

AU - Oliveira E Silva, Diogo

PY - 2014/10

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N2 - We establish the existence of extremizers for a Fourier restriction inequality on planar convex arcs without points with collinear tangents whose curvature satisfies a natural assumption. More generally, we prove that any extremizing sequence of nonnegative functions has a subsequence which converges to an extremizer.

AB - We establish the existence of extremizers for a Fourier restriction inequality on planar convex arcs without points with collinear tangents whose curvature satisfies a natural assumption. More generally, we prove that any extremizing sequence of nonnegative functions has a subsequence which converges to an extremizer.

KW - Nonnegative Function

KW - Decomposition Algorithm

KW - Projection Measure

KW - Optimal Constant

KW - Disjoint Support

UR - https://link.springer.com/article/10.1007%2Fs11854-014-0035-4

U2 - 10.1007/s11854-014-0035-4

DO - 10.1007/s11854-014-0035-4

M3 - Article

SN - 0021-7670

VL - 124

SP - 337

EP - 385

JO - Journal d'Analyse Mathématique

JF - Journal d'Analyse Mathématique

ER -

Extremizers for Fourier restriction inequalities: Convex arcs

Abstract

Keywords

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