Estimation of the uniform norm of one-dimensional Riesz potential of a partial derivative of a function with bounded Laplacian
Ukr. Mat. Zh. - 2016νmber=11. - 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.
Ukr. Mat. Zh. - 2016νmber=11. - 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.
Ukr. Mat. Zh. - 2016νmber=11. - 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
Ukr. Mat. Zh. - 2016νmber=11. - 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.
Ukr. Mat. Zh. - 2016νmber=11. - 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.
Ukr. Mat. Zh. - 2016νmber=11. - 68, № 7. - pp. 945-956
We study the exact asymptotics of almost surely extreme values of discrete random variables.
Ukr. Mat. Zh. - 2016νmber=11. - 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.
Ukr. Mat. Zh. - 2016νmber=11. - 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.
Ukr. Mat. Zh. - 2016νmber=11. - 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
Ukr. Mat. Zh. - 2016νmber=11. - 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.
Ukr. Mat. Zh. - 2016νmber=11. - 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.