S. Tikhonov

activity

20052023

most citedNikolskii inequality and functional classes on compact Lie groups

9 citations · 47 across the 25 of their papers we have counts for

collaborators

Showing 2019Show all

7 papers · 1 filter

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.FA2019

Embeddings and characterizations of Lipschitz spaces

Oscar Domínguez, Dorothee D. Haroske, Sergey Tikhonov

In this paper we give a thorough study of Lipschitz spaces. We obtain the following new results: (1) Sharp Jawerth-Franke-type embeddings between the Besov and Lipschitz spaces ext…

math.FA2019★ 6 cited

Sobolev embeddings, extrapolations, and related inequalities

Oscar Domínguez, Sergey Tikhonov

In this paper we propose a unified approach, based on limiting interpolation, to investigate the embeddings for the Sobolev space $(\dot{W}^k_p(\mathcal{X}))_0, \, \mathcal{X} \in…

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★ 3 cited

Properties of moduli of smoothness in $L_{p} (R^{d})$

Yurii Kolomoitsev, Sergey Tikhonov

In this paper, we discuss various basic properties of moduli of smoothness of functions from $L_{p} (R^{d})$ , $0 < p \leq \infty$ . In particular, complete versions of Jackson-, Mar…

math.CA2019

Nikolskii inequality for lacunary spherical polynomials