Tula State University

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20162019

most citedRiesz potential and maximal function for Dunkl transform

8 citations

researchers with a paper here

collaborating institutions

5 papers

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.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…

math.CA2017★ 8 cited

Riesz potential and maximal function for Dunkl transform

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

We study weighted $(L^{p}, L^{q})$ -boundedness properties of Riesz potentials and fractional maximal functions for the Dunkl transform. In particular, we obtain the weighted Hardy-Litt…

math.CA2016

Doubling condition at the origin for non-negative positive definite functions

Dmitry Gorbachev, Sergey Tikhonov

We study upper and lower estimates as well as the asymptotic behavior of the sharp constant $C = C_{n} (U, V)$ in the doubling-type condition at the origin \[ \frac{1}{|V|}\int_{V}f(x)\,…