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

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18 papers · 1 filter

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.CA2016★ 3 cited

Optimal discrete measures for Riesz potentials

S. V. Borodachov, D. P. Hardin, A. Reznikov +1

For $s ⩾ d$ , we obtain the leading term as $N \to \infty$ of the maximal weighted $N$ -point Riesz $s$ -polarization (or Chebyshev constant) for a certain class of $d$ -rectifia…