2019
Том 71
№ 10

All Issues

Vakarchuk M. B.

Articles: 3
Article (Russian)

On total moduli of continuity for $2\pi$-periodic functions of two variables in the space $L_{2,2}$

Vakarchuk M. B., Vakarchuk S. B.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2017. - 69, № 3. - pp. 300-310

The description of the total moduli of continuity of $2\pi$ -periodic functions of two variables are obtained in the space $L_{2,2}$. The proposed description can be regarded as an extension of the famous results by O. V. Besov, S. B. Stechkin, V. A.Yudin on the moduli of continuity in $L_{2}$ in the two-dimensional case.

Article (Russian)

On the exponential decay of vibrations of damped elastic media

Vakarchuk M. B., Vakarchuk S. B.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 12. - pp. 1579-1601

Exact inequalities of the Kolmogorov type are obtained in Hardy Banach spaces for functions of one complex variable analytic in the unit disk and functions of two complex variables analytic in the unit bidisk. We also present applications of these inequalities to problems of the theory of approximation of analytic functions of one and two complex variables.

Brief Communications (Russian)

On inequalities of Kolmogorov-Hörmander type for functions bounded on a discrete net

Babenko V. F., Vakarchuk M. B.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 7. - pp. 988–992

We obtain a strengthened version of the Hörmander inequality for functions ƒ: ℝ → ℝ, in which, instead of ‖ƒ‖, we use the least upper bound of the values of f on a discrete set of points.