9 citations · 47 across the 25 of their papers we have counts for
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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…
Nikolskii inequality and functional classes on compact Lie groups
E. D. Nursultanov, M. V. Ruzhansky, S. Yu. Tikhonov
In this note we study Besov, Triebel-Lizorkin, Wiener, and Beurling function spaces on compact Lie groups. A major role in the analysis is played by the Nikolskii inequality.
Pitt's inequalities and uncertainty principle for generalized Fourier transform
Dmitry Gorbachev, Valery Ivanov, Sergey Tikhonov
We study the two-parameter family of unitary operators \[ \mathcal{F}_{k,a}=\exp\Bigl(\frac{iπ}{2a}\,(2\langle k\rangle+{d}+a-2 )\Bigr) \exp\Bigl(\frac{iπ}{2a}\,Δ_{k,a}\Bigr), \] w…
Sharp Pitt inequality and logarithmic uncertainty principle for Dunkl transform in
Dmitry Gorbachev, Valery Ivanov, Sergey Tikhonov
We prove sharp Pitt's inequality for the Dunkl transform in with the corresponding weights. As an application, we obtain the logarithmic uncertainty princip…