Tula State University

output

20092019

most citedOn a bound of the absolute constant in the Berry--Esseen inequality for i.i.d. Bernoulli random variables

17 citations

11 papers

math.CA2019

Sharp approximation theorems and Fourier inequalities in the Dunkl setting

D. V. Gorbachev, V. I. Ivanov, S. Yu. Tikhonov

In this paper we study direct and inverse approximation inequalities in $L^{p} (R^{d})$ , $1 < p < \infty$ , with the Dunkl weight. We obtain these estimates in their sharp form…

math.CA2019★ 5 cited

Estimates of the asymptotic Nikolskii constants for spherical polynomials

Feng Dai, Dmitry Gorbachev, Sergey Tikhonov

Let $Π_{n}^{d}$ denote the space of spherical polynomials of degree at most $n$ on the unit sphere $S^{d} \subset R^{d + 1}$ that is equipped with the surface Lebesgue mea…

math.CA2019

Nikolskii inequality for lacunary spherical polynomials

Feng Dai, Dmitry Gorbachev, Sergey Tikhonov

We prove that for $d \geq 2$ , the asymptotic order of the usual Nikolskii inequality on $S^{d}$ (also known as the reverse Hölder's inequality) can be significantly improved i…

math.CA2018

Fractional smoothness in $L^{p}$ with Dunkl weight and its applications

D. V. Gorbachev, V. I. Ivanov

We define fractional power of the Dunkl Laplacian, fractional modulus of smoothness and fractional $K$ -functional in $L^{p}$ -space with the Dunkl weight. As application, we prove dir…

math.PR2018★ 17 cited

On a bound of the absolute constant in the Berry--Esseen inequality for i.i.d. Bernoulli random variables

Anatolii Zolotukhin, Sergei Nagaev, Vladimir Chebotarev

It is shown that the absolute constant in the Berry--Esseen inequality for i.i.d. Bernoulli random variables is strictly less than the Esseen constant, if $1 \leq n \leq 500000$ , where…

math.CA2017★ 3 cited

Nikolskii constants for polynomials on the unit sphere

Feng Dai, Dmitry Gorbachev, Sergey Tikhonov

This paper studies the asymptotic behavior of the exact constants of the Nikolskii inequalities for the space $Π_{n}^{d}$ of spherical polynomials of degree at most $n$ on the unit sph…

Sharp approximation theorems and Fourier inequalities in the Dunkl setting

Estimates of the asymptotic Nikolskii constants for spherical polynomials

Nikolskii inequality for lacunary spherical polynomials

Fractional smoothness in Lp with Dunkl weight and its applications

On a bound of the absolute constant in the Berry--Esseen inequality for i.i.d. Bernoulli random variables

Nikolskii constants for polynomials on the unit sphere

Fractional smoothness in $L^{p}$ with Dunkl weight and its applications