5 citations · 16 across the 9 of their papers we have counts for
14 papers
New estimates for the maximal functions and applications
Oscar Domínguez, Sergey Tikhonov
In this paper we study sharp pointwise inequalities for maximal operators. In particular, we strengthen DeVore's inequality for the moduli of smoothness and a logarithmic variant o…
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 , , with the Dunkl weight. We obtain these estimates in their sharp form…
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…
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…
Estimates of the asymptotic Nikolskii constants for spherical polynomials
Feng Dai, Dmitry Gorbachev, Sergey Tikhonov
Let denote the space of spherical polynomials of degree at most on the unit sphere that is equipped with the surface Lebesgue mea…
Properties of moduli of smoothness in
Yurii Kolomoitsev, Sergey Tikhonov
In this paper, we discuss various basic properties of moduli of smoothness of functions from , . In particular, complete versions of Jackson-, Mar…