2019
Том 71
№ 5

All Issues

Kolomoitsev Yu. S.

Articles: 3
Article (Russian)

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

Kolomoitsev Yu. S.

↓ Abstract   |   Full text (.pdf)

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

Kolomoitsev Yu. S.

↓ Abstract   |   Full text (.pdf)

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 $L_p, 0 < p < 1$

Kolomoitsev Yu. S.

↓ Abstract   |   Full text (.pdf)

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.