A sharp nonlinear Hausdorff-Young inequality for small potentials

Diogo Oliveira E Silva; Vjekoslav Kovac; Jelena Rupcic

doi:10.1090/proc/14268

A sharp nonlinear Hausdorff-Young inequality for small potentials

Diogo Oliveira E Silva, Vjekoslav Kovac, Jelena Rupcic

Mathematics

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Abstract

The nonlinear Hausdorff-Young inequality follows from the work of Christ and Kiselev. Later Muscalu, Tao, and Thiele asked if the constants can be chosen independently of the exponent. We show that the nonlinear Hausdorff-Young quotient admits an even better upper bound than the linear one, provided that the function is sufficiently small in the L¹ norm. The proof combines perturbative techniques with the sharpened version of the linear Hausdorff-Young inequality due to Christ.

Original language	English
Pages (from-to)	239-253
Journal	Proceedings of the American Mathematical Society
Volume	147
Early online date	3 Oct 2018
DOIs	https://doi.org/10.1090/proc/14268
Publication status	E-pub ahead of print - 3 Oct 2018

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10.1090/proc/14268

Kovac_et_al_Sharp_Nonlinear_Hausdorff-Young_PAMS
First published in Proc. Amer. Math. Soc. 147 (2019), 239-253 published by the American Mathematical Society. © 2016 American Mathematical Society https://doi.org/10.1090/proc/14268 checked on 6/12/18
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https://arxiv.org/abs/1703.05557

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title = "A sharp nonlinear Hausdorff-Young inequality for small potentials",

abstract = "The nonlinear Hausdorff-Young inequality follows from the work of Christ and Kiselev. Later Muscalu, Tao, and Thiele asked if the constants can be chosen independently of the exponent. We show that the nonlinear Hausdorff-Young quotient admits an even better upper bound than the linear one, provided that the function is sufficiently small in the L1 norm. The proof combines perturbative techniques with the sharpened version of the linear Hausdorff-Young inequality due to Christ.",

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AB - The nonlinear Hausdorff-Young inequality follows from the work of Christ and Kiselev. Later Muscalu, Tao, and Thiele asked if the constants can be chosen independently of the exponent. We show that the nonlinear Hausdorff-Young quotient admits an even better upper bound than the linear one, provided that the function is sufficiently small in the L1 norm. The proof combines perturbative techniques with the sharpened version of the linear Hausdorff-Young inequality due to Christ.

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JO - Proceedings of the American Mathematical Society

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A sharp nonlinear Hausdorff-Young inequality for small potentials

Abstract

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