2019
Том 71
№ 11

All Issues

Hembars'ka S. B.

Articles: 6
Article (Ukrainian)

On boundary values of three-harmonic Poisson integral on the boundary of a unit disk

Hembars'ka S. B.

↓ Abstract

Ukr. Mat. Zh. - 2018. - 70, № 7. - pp. 876-884

Let $C_0$ be a curve in a disk $D = \{ | z| < 1\}$ tangential to a circle at the point $z = 1$ and let $C_{\theta}$ be the result of rotation of this curve about the origin $z = 0$ by an angle \theta . We construct a bounded function $u(z)$ three-harmonic in $D$ with zero normal derivatives $\cfrac{\partial u}{\partial n}$ and $\cfrac{\partial 2u}{\partial r_2}$ on the boundary such that the limit along $C_{\theta}$ does not exist for all $\theta , 0 \leq \theta \leq 2\pi $.

Article (Ukrainian)

Approximative properties of biharmonic Poisson integrals on Hölder classes

Hembars'ka S. B., Zhyhallo K. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2017. - 69, № 7. - pp. 925-932

We establish asymptotic expansions for the values of approximation of functions from the H¨older class by biharmonic Poisson integrals in the uniform and integral metrics.

Article (Ukrainian)

Estimations of the integral of modulus for mixed derivatives of the sum of double trigonometric series

Hembars'ka S. B., Zaderei P. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2016. - 68, № 7. - pp. 908-921

For functions of two variables defined by trigonometric series with quasiconvex coefficients, we estimate their variations in the Hardy – Vitali sense.

Article (Russian)

Estimates for the Variation of Functions Defined by Double Trigonometric Cosine Series

Hembars'ka S. B.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2003. - 55, № 6. - pp. 733-749

For functions of two variables defined by trigonometric cosine series with quasiconvex coefficients, we obtain estimates for their variations in the Hardy–Vitali sense.

Article (Ukrainian)

On the absolute convergence of power series

Hembars'ka S. B., Zaderei P. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1999. - 51, № 5. - pp. 594–602

We obtain a two-dimensional analog of the Hardy-Littlewood result on the absolute convergence of power series in the case of multiple series on the boundary of a unit polydisk.

Article (Ukrainian)

Tangential limit values of a biharmonic poisson integral in a disk

Hembars'ka S. B.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 9. - pp. 1171–1176

Let C 0 be a curve in a disk D={|z|<1} that is tangent to the circle at the point z=1, and let C θ be the result of rotation of this curve about the origin z=0 by an angle θ. We construct a bounded function biharmonic in D that has a zero normal derivative on the boundary and for which the limit along C θ does not exist for all θ, 0≤θ≤2π.