Pitt inequalities and restriction theorems for the Fourier transform

Laura De Carli; Dmitry Gorbachev; Sergey Tikhonov

doi:10.4171/rmi/955

Pitt inequalities and restriction theorems for the Fourier transform

Laura De Carli, Dmitry Gorbachev, Sergey Tikhonov

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

6 Citations (Scopus)

Abstract

© 2017 European Mathematical Society. We prove new Pitt inequalities for the Fourier transforms with radial and non-radial weights using weighted restriction inequalities for the Fourier transform on the sphere. We also prove new Riemann-Lebesgue estimates and versions of the uncertainty principle for the Fourier transform.

Original language	English
Pages (from-to)	789-808
Journal	Revista Matematica Iberoamericana
Volume	33
Issue number	3
DOIs	https://doi.org/10.4171/rmi/955
Publication status	Published - 1 Jan 2017

Keywords

Pitt inequalities
Restriction theorems
Riemann-Lebesgue estimate
Uncertainty principle
Weights

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10.4171/rmi/955

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title = "Pitt inequalities and restriction theorems for the Fourier transform",

abstract = "{\textcopyright} 2017 European Mathematical Society. We prove new Pitt inequalities for the Fourier transforms with radial and non-radial weights using weighted restriction inequalities for the Fourier transform on the sphere. We also prove new Riemann-Lebesgue estimates and versions of the uncertainty principle for the Fourier transform.",

keywords = "Pitt inequalities, Restriction theorems, Riemann-Lebesgue estimate, Uncertainty principle, Weights",

author = "{De Carli}, Laura and Dmitry Gorbachev and Sergey Tikhonov",

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journal = "Revista Matematica Iberoamericana",

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AU - De Carli, Laura

AU - Gorbachev, Dmitry

AU - Tikhonov, Sergey

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N2 - © 2017 European Mathematical Society. We prove new Pitt inequalities for the Fourier transforms with radial and non-radial weights using weighted restriction inequalities for the Fourier transform on the sphere. We also prove new Riemann-Lebesgue estimates and versions of the uncertainty principle for the Fourier transform.

AB - © 2017 European Mathematical Society. We prove new Pitt inequalities for the Fourier transforms with radial and non-radial weights using weighted restriction inequalities for the Fourier transform on the sphere. We also prove new Riemann-Lebesgue estimates and versions of the uncertainty principle for the Fourier transform.

KW - Pitt inequalities

KW - Restriction theorems

KW - Riemann-Lebesgue estimate

KW - Uncertainty principle

KW - Weights

U2 - 10.4171/rmi/955

DO - 10.4171/rmi/955

M3 - Article

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EP - 808

JO - Revista Matematica Iberoamericana

JF - Revista Matematica Iberoamericana

SN - 0213-2230

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