2 papers
math.CA2016
Wiener's problem for positive definite functions
Dmitry Gorbachev, Sergey Tikhonov
We study the sharp constant in Wiener's inequality for positive definite functions \[ \int_{\mathbb{T}^{n}}|f|^{2}\,dx\le W_{n}(D)|D|^{-1}\int_{D}|f|^{2}\,dx,\quad D\sub…
math.FA2015
Pitt inequalities and restriction theorems for the Fourier transform
Laura De Carli, Dmitriy 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 als…