Revista Matemática Iberoamericana

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Volume 33, Issue 3, 2017, pp. 789–808
DOI: 10.4171/RMI/955

Pitt inequalities and restriction theorems for the Fourier transform

Laura De Carli[1], Dmitry Gorbachev[2] and Sergey Tikhonov[3]

(1) Florida International University, Miami, USA
(2) Tula State University, Russia
(3) Universitat Autònoma de Barcelona and ICREA, Barcelona, Spain

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, weights, Riemann–Lebesgue estimate, uncertainty principle

De Carli Laura, Gorbachev Dmitry, Tikhonov Sergey: Pitt inequalities and restriction theorems for the Fourier transform. Rev. Mat. Iberoamericana 33 (2017), 789-808. doi: 10.4171/RMI/955