Nonexistence of extremizers for certain convex curves

Diogo Oliveira e Silva

doi:10.4310/MRL.2018.v25.n3.a12

Nonexistence of extremizers for certain convex curves

Diogo Oliveira e Silva

Mathematics

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

Abstract

We establish the nonexistence of extremizers for a local Fourier restriction inequality on a certain class of planar convex curves whose curvature satisfies a natural assumption. We accomplish this by studying the local behavior of the triple convolution of the arclength measure on the curve with itself, and show in particular that every extremizing sequence concentrates at a point on the curve.

Original language	English
Pages (from-to)	973-987
Journal	Mathematical Research Letters
Volume	25
Issue number	3
DOIs	https://doi.org/10.4310/MRL.2018.v25.n3.a12
Publication status	Published - 1 Mar 2018

Bibliographical note

11 pages

Keywords

math.CA
math.AP
42A05
extremizers
Tomas-Stein inequality
convolution of arclength measure

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abstract = "We establish the nonexistence of extremizers for a local Fourier restriction inequality on a certain class of planar convex curves whose curvature satisfies a natural assumption. We accomplish this by studying the local behavior of the triple convolution of the arclength measure on the curve with itself, and show in particular that every extremizing sequence concentrates at a point on the curve.",

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AB - We establish the nonexistence of extremizers for a local Fourier restriction inequality on a certain class of planar convex curves whose curvature satisfies a natural assumption. We accomplish this by studying the local behavior of the triple convolution of the arclength measure on the curve with itself, and show in particular that every extremizing sequence concentrates at a point on the curve.

KW - math.CA

KW - math.AP

KW - 42A05

KW - extremizers

KW - Tomas-Stein inequality

KW - convolution of arclength measure

U2 - 10.4310/MRL.2018.v25.n3.a12

DO - 10.4310/MRL.2018.v25.n3.a12

M3 - Article

SN - 1073-2780

VL - 25

SP - 973

EP - 987

JO - Mathematical Research Letters

JF - Mathematical Research Letters

IS - 3

ER -

Nonexistence of extremizers for certain convex curves

Abstract

Bibliographical note

Keywords

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Cite this