2019
Том 71
№ 11

# Hembars'ka S. B.

Articles: 6
Article (Ukrainian)

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

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

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

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

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

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

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.