2017
Том 69
№ 9

# Ukrains’kyi Matematychnyi Zhurnal (Ukrainian Mathematical Journal)

Editor-in-Chief: A. M. Samoilenko
ISSN: 0041-6053, 1027-3190

Ukrains'kyi Matematychnyi Zhurnal (UMZh) was founded in May 1949. Journal is issued by Institute of Mathematics NAS of Ukraine. English version is reprinted in the Springer publishing house and called Ukrainian Mathematical Journal.

Ukrains'kyi Matematychnyi Zhurnal focuses on research papers in the principal fields of pure and applied mathematics. The journal is published monthly, each annual volume consists of 12 issues. Articles in Ukrainian, Russian and English are accepted for review.

UMZh indexed in: MathSciNet, zbMATH, Scopus, Web of Science, Google Scholar.

Impact Factor*: 0.189
*2015 Journal Citation Reports, Thomson Reuters

SCImago Journal Rank (SJR) 2015: 0.31; H-index: 13
Source Normalized Impact per Paper (SNIP) 2014: 0.605
Impact per Publication (IPP) 2014: 0.216

Mathematical Citation Quotient (MCQ) 2014: 0.22

## Latest Articles (September 2017)

Brief Communications (Ukrainian)

### Karamata integral representations for functions generalizing regularly varying functions

Ukr. Mat. Zh. - 2017. - 69, № 9. - pp. 1289-1296

We consider the classes of functions that generalized regularly varying and receive Karamata’s type integral representations for this functions.

Article (English)

### Boundedness of Riesz-type potential operators on variable exponent Herz – Morrey spaces

Ukr. Mat. Zh. - 2017. - 69, № 9. - pp. 1187-1197

We show the boundedness of the Riesz-type potential operator of variable order $\beta (x)$ from the variable exponent Herz – Morrey spaces $M \dot{K}^{\alpha (\cdot ),\lambda}_{p_1 ,q_1 (\cdot )}(\mathbb{R}^n)$ into the weighted space $M \dot{K}^{\alpha (\cdot ),\lambda}_{p_2 ,q_2 (\cdot )}(\mathbb{R}^n, \omega )$, where $\alpha (x) \in L^{\infty} (\mathbb{R}^n) is log-Holder continuous both at the origin and at infinity,$\omega = (1+| x| ) \gamma (x)$with some$\gamma (x) > 0$, and$1/q_1 (x) 1/q_2 (x) = \beta (x)/n$when$q_1 (x)$is not necessarily constant at infinity. It is assumed that the exponent$q_1 (x)$satisfies the logarithmic continuity condition both locally and at infinity and$1 < (q_1)_{\infty} \leq q_1(x) \leq (q_1)_+ < \infty, \;x \in \mathbb{R}\$.

Brief Communications (English)

### Well-posedness of the Dirichlet problem in a cylindrical domain for three-dimensional elliptic equations with degeneration of type and order

Ukr. Mat. Zh. - 2017. - 69, № 9. - pp. 1270-1274

The paper shows the unique solvability of the classical Dirichlet problem in cylindrical domain for three-dimensional elliptic equations with degeneration type and order.