Revista Matemática Iberoamericana
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Pitt inequalities and restriction theorems for the Fourier transformLaura De Carli, Dmitry Gorbachev and Sergey Tikhonov (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