Resumen de Pitt inequalities and restriction theorems for the Fourier transform

Laura De Carli, Dmitry Gorbachev, Sergey Tikhonov

• 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.