Sergey Tikhonov

activity

20122015

most citedReverse Hölder's inequality for spherical harmonics

2 citations · 4 across the 4 of their papers we have counts for

collaborators

4 papers

math.CA2015★ 2 cited

Sharp Pitt inequality and logarithmic uncertainty principle for Dunkl transform in $L^{2}$

Dmitry Gorbachev, Valery Ivanov, Sergey Tikhonov

We prove sharp Pitt's inequality for the Dunkl transform in $L^{2} (R^{d})$ with the corresponding weights. As an application, we obtain the logarithmic uncertainty princip…

math.CA2014★ 2 cited

Reverse Hölder's inequality for spherical harmonics

Feng Dai, Han Feng, Sergey Tikhonov

This paper determines the sharp asymptotic order of the following reverse Hölder inequality for spherical harmonics $Y_{n}$ of degree $n$ on the unit sphere $S^{d - 1}$ of $\m…

math.CA2012

Moduli of smoothness and growth properties of Fourier transforms: two-sided estimates

D. Gorbachev, S. Tikhonov

We prove two-sided inequalities between the integral moduli of smoothness of a function on $R^{d} / T^{d}$ and the weighted tail-type integrals of its Fourier transform…

math.AP2012

Regularity of the Monge-Ampère equation in Besov's space

Alexander V. Kolesnikov, Sergey Yu. Tikhonov

Let $μ = e^{- V} d x$ be a probability measure and $T = \nablaΦ$ be the optimal transportation mapping pushing forward $μ$ onto a log-concave compactly supported measure $ν= e^{-W}…

Sharp Pitt inequality and logarithmic uncertainty principle for Dunkl transform in L2

Reverse Hölder's inequality for spherical harmonics

Moduli of smoothness and growth properties of Fourier transforms: two-sided estimates

Regularity of the Monge-Ampère equation in Besov's space

Sharp Pitt inequality and logarithmic uncertainty principle for Dunkl transform in $L^{2}$