Pitt inequalities and restriction theorems for the Fourier transform
Laura De Carli
Florida International University, Miami, USADmitry Gorbachev
Tula State University, RussiaSergey 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