Pitt inequalities and restriction theorems for the Fourier transform

Laura De Carli; Dmitry Gorbachev; Sergey Tikhonov

doi:10.4171/rmi/955

JournalsrmiVol. 33, No. 3pp. 789–808

Pitt inequalities and restriction theorems for the Fourier transform

Laura De Carli
Florida International University, Miami, USA
- MathSciNet
- zbMATH Open
Dmitry Gorbachev
Tula State University, Russia
- MathSciNet
- zbMATH Open
Sergey Tikhonov
Universitat Autònoma de Barcelona and ICREA, Barcelona, Spain
- MathSciNet
- zbMATH Open

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Abstract

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.

Cite this article

Laura De Carli, Dmitry Gorbachev, Sergey Tikhonov, Pitt inequalities and restriction theorems for the Fourier transform. Rev. Mat. Iberoam. 33 (2017), no. 3, pp. 789–808

DOI 10.4171/RMI/955