# Volume 68, № 7, 2016

### Estimation of the uniform norm of one-dimensional Riesz potential of a partial derivative of a function with bounded Laplacian

Babenko V. F., Parfinovych N. V.

↓ Abstract

Ukr. Mat. Zh. - 2016. - 68, № 7. - pp. 867-878

We obtain new exact Landau-type estimates for the uniform norms of one-dimension Riesz potentials of the partial derivatives of a multivariable function in terms of the norm of the function itself and the norm of its Laplacian.

### Refinements of Jessen’s functional

Barbir A., Himmelreich Kruli´c K., Pečarić J. E.

↓ Abstract

Ukr. Mat. Zh. - 2016. - 68, № 7. - pp. 879-896

We obtain new refinements of Jessen’s functional defined by means of positive linear functionals. The accumulated results are then applied to weighted generalized and power means. We also obtain new refinements of numerous classical inequalities such as the arithmetic-geometric mean inequality, Young’s inequality, and H¨older’s inequality.

### Laplacian with respect to measure on a Riemannian manifold and Dirichlet problem. I

Bogdanskii Yu. V., Potapenko A. Yu.

↓ Abstract

Ukr. Mat. Zh. - 2016. - 68, № 7. - pp. 897-907

We propose an $L^2$ -version of the Laplacian with respect to measure on an infinite-dimensional Riemannian manifold. The Dirichlet problem for equations with proposed Laplacian is solved in the region of a Rimannian manifold from a certain class.

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

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

↓ Abstract

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.

### Automorphisms and derivations of Leibniz algebras

Ladra M., Rikhsiboev I. M., Turdibaev R. M.

↓ Abstract

Ukr. Mat. Zh. - 2016. - 68, № 7. - pp. 933-944

We extend some general properties of automorphisms and derivations known for the Lie algebras to finite-dimensional complex Leibniz algebras. The analogs of the Jordan – Chevalley decomposition for derivations and the multiplicative decomposition for automorphisms of finite-dimensional complex Leibniz algebras are obtained.

### Asymptotic behavior of the extreme values of random variables. Discrete case

↓ Abstract

Ukr. Mat. Zh. - 2016. - 68, № 7. - pp. 945-956

We study the exact asymptotics of almost surely extreme values of discrete random variables.

### Finitely solvable groups with nilpotent wide subgroups

↓ Abstract

Ukr. Mat. Zh. - 2016. - 68, № 7. - pp. 957-962

A subgroup $H$ of a finite group $G$ is called wide if each prime divisor of the order of $G$ divides the order of $H$. We obtain a description of finite solvable groups without wide subgroups. It is shown that a finite solvable group with nilpotent wide subgroups contains a quotient group with respect to the hypercenter without wide subgroups.

### Slant lightlike submersions from an indefinite almost Hermitian manifold onto a lightlike manifold

Bhatia S. S., Kumar R., Sachdeva R.

↓ Abstract

Ukr. Mat. Zh. - 2016. - 68, № 7. - pp. 963-971

We introduce slant lightlike submersions from an indefinite almost Hermitian manifold onto a lightlike manifold. We establish existence theorems for these submersions. We also investigate the necessary and sufficient conditions for the leaves of the distributions to be totally geodesic foliations in indefinite almost Hermitian manifolds.

### Inverse coefficient problem fоr a two-dimensional parabolic equation in a domain with free boundary

↓ Abstract

Ukr. Mat. Zh. - 2016. - 68, № 7. - pp. 972-982

We establish the conditions of unique solvability of the inverse problem of finding the minor coefficient in a two-dimensional parabolic equation in the domain for which the location of a part of its boundary is described by a function in the form of a product of an unknown function of time and a given function of the space variable.

### Best $m$-term trigonometric approximation for periodic functions with low mixed smoothness from the Nikol’skii – Besov-type classes

↓ Abstract

Ukr. Mat. Zh. - 2016. - 68, № 7. - pp. 983-1003

We establish the exact-order estimates of the best $m$-term trigonometric approximation for periodic multivariable functions (with low mixed smoothness) from the Nikol’skii – Besov-type classes.

### A new application of quasimonotone sequences

↓ Abstract

Ukr. Mat. Zh. - 2016. - 68, № 7. - pp. 1004-1008

We prove a general theorem dealing with generalized absolute Ces`aro summability factors of infinite series. This theorem also includes some new and known results.