2019
Том 71
№ 9

# Kolomoitsev Yu. S.

Articles: 3
Article (Russian)

### Inequalities for the Fractional Derivatives of Trigonometric Polynomials in Spaces with Integral Metrics

Ukr. Mat. Zh. - 2015. - 67, № 1. - pp. 42-56

We establish necessary and sufficient conditions for the validity of Bernstein-type inequalities for the fractional derivatives of trigonometric polynomials of several variables in spaces with integral metrics. The problem of sharpness of these inequalities is investigated.

Article (Russian)

### Generalization of One Sufficient Condition for Fourier Multipliers

Ukr. Mat. Zh. - 2012. - 64, № 10. - pp. 1373-1380

We obtain new sufficient conditions for Fourier multipliers in the Hardy spaces $H_p(\mathbb{R}^n),\; 0 < p < 2$. These conditions are given in terms of the simultaneous behavior of a function and its derivatives. The results of this paper generalize the corresponding theorems of A. Miachi.

Article (Russian)

### On moduli of smoothness and Fourier multipliers in $L_p, 0 < p < 1$

Ukr. Mat. Zh. - 2007. - 59, № 9. - pp. 1221–1238

We obtain the theorem on the relationship between a modulus of smoothness and the best approximation in L p , 0 < p < 1, and theorems on the extension of functions with the preservation of the modulus of smoothness in L p , 0 < p < 1.
In addition, we present a complete description of multipliers of periodic functions in the spaces L p , 0 < p < 1.