D. Gorbachev

activity

20022026

most citedRiesz potential and maximal function for Dunkl transform

8 citations · 30 across the 19 of their papers we have counts for

collaborators

Showing 2019 · math.CAShow all

4 papers · 2 filters

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.CA2019★ 3 cited

Uncertainty principles for eventually constant sign bandlimited functions

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

We study the uncertainty principles related to the generalized Logan problem in $R^{d}$ . Our main result provides the complete solution of the following problem: for a fix…