A. Reznikov

activity

20102020

most citedOn weak weighted estimates of martingale transform

18 citations · 95 across the 21 of their papers we have counts for

collaborators

23 papers

math.CA2020

Minimal Riesz energy on balanced fractal sets

Austin Anderson, Alexander Reznikov

We investigate the asymptotic behavior of minimal $N$ -point Riesz $s$ -energy on fractal sets of non-integer dimension, with algebraically dependent contraction ratios. For $s$ bigg…

math.CA2018

Riesz energy on self-similar sets

Alexander Reznikov, Oleksandr Vlasiuk

We investigate properties of minimal $N$ -point Riesz $s$ -energy on fractal sets of non-integer dimension, as well as asymptotic behavior of $N$ -point configurations that minimize t…

math.CA2018

Dimension free properties of strong Muckenhoupt and Reverse Hölder weights for Radon measures

Oleksandra Beznosova, Alexander Reznikov

In this paper we prove self-improvement properties of strong Muckenhoupt and Reverse Hölder weights with respect to a general Radon measure on $R^{n}$ . We derive our result…

math.CA2017★ 2 cited

Local properties of Riesz minimal energy configurations and equilibrium measures

D. P. Hardin, A. Reznikov, E. B. Saff +1

We investigate separation properties of $N$ -point configurations that minimize discrete Riesz $s$ -energy on a compact set $A \subset R^{p}$ . When $A$ is a smooth $(p - 1)$ -dime…

math.CA2017

Covering and separation of Chebyshev points for non-integrable Riesz potentials

Alexander Reznikov, Edward B. Saff, Alexander Volberg

For Riesz $s$ -potentials $K (x, y) = ∣ x - y ∣^{- s}$ , $s > 0$ , we investigate separation and covering properties of $N$ -point configurations $ω_{N}^{*} = {x_{1}, \dots, x_{N}}$ on a $d$ -dimensional…

math.AP2016★ 18 cited

On weak weighted estimates of martingale transform

Fedor Nazarov, Alexander Reznikov, Vasily Vasyunin +1

We consider several weak type estimates for singular operators using the Bellman function approach. We disprove the $A_{1}$ conjecture of Muckenhoupt, which stayed open after Muckenh…