JournalsrmiVol. 33, No. 3pp. 789–808

Pitt inequalities and restriction theorems for the Fourier transform

  • Laura De Carli

    Florida International University, Miami, USA

  • Dmitry Gorbachev

    Tula State University, Russia

  • Sergey Tikhonov

    Universitat Autònoma de Barcelona and ICREA, Barcelona, Spain
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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