Maximizers for the Stein–Tomas Inequality

Rupert L. Frank; Elliott H. Lieb; Julien Sabin

doi:10.1007/s00039-016-0380-9

Maximizers for the Stein–Tomas Inequality

Rupert L. Frank
, Elliott H. Lieb
, Julien Sabin

Mathematics

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

33 Scopus citations

Abstract

We give a necessary and sufficient condition for the precompactness of all optimizing sequences for the Stein–Tomas inequality. In particular, if a well-known conjecture about the optimal constant in the Strichartz inequality is true, we obtain the existence of an optimizer in the Stein–Tomas inequality. Our result is valid in any dimension.

Original language	English (US)
Pages (from-to)	1095-1134
Number of pages	40
Journal	Geometric and Functional Analysis
Volume	26
Issue number	4
DOIs	https://doi.org/10.1007/s00039-016-0380-9
State	Published - Jul 1 2016

All Science Journal Classification (ASJC) codes

Analysis
Geometry and Topology

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10.1007/s00039-016-0380-9

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title = "Maximizers for the Stein–Tomas Inequality",

abstract = "We give a necessary and sufficient condition for the precompactness of all optimizing sequences for the Stein–Tomas inequality. In particular, if a well-known conjecture about the optimal constant in the Strichartz inequality is true, we obtain the existence of an optimizer in the Stein–Tomas inequality. Our result is valid in any dimension.",

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T1 - Maximizers for the Stein–Tomas Inequality

AU - Frank, Rupert L.

AU - Lieb, Elliott H.

AU - Sabin, Julien

PY - 2016/7/1

Y1 - 2016/7/1

N2 - We give a necessary and sufficient condition for the precompactness of all optimizing sequences for the Stein–Tomas inequality. In particular, if a well-known conjecture about the optimal constant in the Strichartz inequality is true, we obtain the existence of an optimizer in the Stein–Tomas inequality. Our result is valid in any dimension.

AB - We give a necessary and sufficient condition for the precompactness of all optimizing sequences for the Stein–Tomas inequality. In particular, if a well-known conjecture about the optimal constant in the Strichartz inequality is true, we obtain the existence of an optimizer in the Stein–Tomas inequality. Our result is valid in any dimension.

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UR - https://www.scopus.com/pages/publications/84990859041#tab=citedBy

U2 - 10.1007/s00039-016-0380-9

DO - 10.1007/s00039-016-0380-9

M3 - Article

AN - SCOPUS:84990859041

SN - 1016-443X

VL - 26

SP - 1095

EP - 1134

JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

IS - 4

ER -

Maximizers for the Stein–Tomas Inequality

Abstract

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