Eurasian Mathematical Journal

Hölder inequality on the space of upper semicontinuous functions

Sh.A. Ayupov, M.R. Eshimbetov, A.A. Zaitov — Tue, 31 Mar 2026 00:00:00 +0000

For a compact Hausdorff space X, we consider the space IB(X) of all idempotent probability measures on X, which are defined as set-functions on the σ-algebra of all Borel subsets of X, and also the space IUSC(X) of all normalized max-plus linear functionals on the linear space of all upper semicontinuous functions on X, equipped with idempotent operations. In the main result it is established that a max-plus version of the Hölder inequality holds on the space of upper semicontinuous functions.

p-numerical radius inequalities for the tensor product of operators

A. Frakis, F. Kittaneh, S. Soltani — Tue, 31 Mar 2026 00:00:00 +0000

In this paper, we give several inequalities for the tensor product of two operators involving the p-numerical radius and the Schatten p-norms.

Adams theorem for the B-Riesz potential in the total B-Morrey spaces

V.S. Guliyev, A. Akbulut, M.N. Omarova, A. Serbetci — Tue, 31 Mar 2026 00:00:00 +0000

We prove Adams theorem for the Riesz potential \(I_{\gamma}^{\alpha}\) (B-Riesz potential) in the total Morrey spaces \(L_{p,(\lambda,\mu),\gamma}\) (total B-Morrey spaces), associated with the Laplace-Bessel differential operator \(\Delta_B\). More precisely, we obtain necessary and sufficient conditions for the operator \(I_{\gamma}^{\alpha}\) to be bounded from the total B-Morrey space \(L_{p,(\lambda,\mu),\gamma}\) to the total B-Morrey space \(L_{q,(\lambda,\mu),\gamma}\) and from the total B-Morrey space \(L_{1,(\lambda,\mu),\gamma}\) to the weak total B-Morrey space \(WL_{q,(\lambda,\mu),\gamma}\).

Anisotropic Morrey-type spaces and their interpolation properties

J.G. Jumabayeva, E.D. Nursultanov — Tue, 31 Mar 2026 00:00:00 +0000

In this paper, there are defined the anisotropic local Morrey-type spaces \(LM_{\bar{p},\bar{q}}^{\bar{\lambda}}\) and the anisotropic generalized Morrey-type spaces \(M_{\bar{p},\bar{q}}^{\bar{\lambda}}\), where \(\bar{p}\), \(\bar{q}\), and \(\bar{\lambda}\) are vectors. The spaces \(LM_{\bar{p},\bar{q}}^{\bar{\lambda}}\) allow relaxation of the conditions on the parameter \(\bar{\lambda}\), namely, the components of the given vector can take any real value, i.e., \(-\infty < \lambda_i < \infty,\ i = 1, \overline{d}\), in contrast to previously studied spaces. The embedding properties of the defined spaces are investigated. Additionally, an anisotropic interpolation method is considered, which allows the study of the interpolation properties of these spaces.

Combining unsupervised dimension reduction with sufficient dimension reduction

Zh. Mukanov, A. Sharafudinov, R. Takhanov, A. Bekembayev — Tue, 31 Mar 2026 00:00:00 +0000

We present a new method for dimension reduction that combines unsupervised dimension reduction (UDR) with sufficient dimension reduction (SDR). In unsupervised dimension reduction the goal is to find a low-dimensional linear subspace that approximates the support of a data distribution. If data is supervised, then in sufficient dimension reduction the goal is to find a low-dimensional linear subspace, called the effective subspace, such that the projection of an input vector onto that subspace maximally captures information on correlations between an input and an output.

The objective that we suggest to minimize consists of two parts. The first one is responsible for the UDR part, it forces a low-dimensional probabilistic measure \(\mu\) to approximate a distribution over inputs. The second one is responsible for the SDR part, it forces a regression function \(f\) to be consistent with supervised data. Additionally, we require the support of \(\mu\) and the effective subspace of \(f\) to be equal. In this hybrid setting we solve two problems, UDR and SDR, so that the UDR term serves as a regularizer of the SDR term.

We reformulate the problem as an optimization task of finding a \(k\)-dimensional linear subspace \(S\) and a pair of complex measures \((\mu,\mu')\) supported in \(S\). Instead of optimizing over complex measures, we suggest minimizing over ordinary functions \((g_1,g_2)\) but with an additional term \(R\) that penalizes a distortion of the common support of \(g_1,g_2\) from a \(k\)-dimensional linear subspace. The algorithm that we develop can be formulated for functions \((g_1,g_2)\) as well as for their inverse Fourier transforms. Eventually, we report results of numerical experiments on well-known datasets.

Generalizations of Hardy-type integral inequalities for quasimonotone functions in weighted variable exponent Lebesgue spaces

M. Sofrani, A. Senouci — Tue, 31 Mar 2026 00:00:00 +0000

In 1992 V.I. Burenkov proved some Hardy's inequalities with sharp constants in Lebesgue spaces for monotone functions for \(0 < p < 1\). Later R.A. Bandaliev established analogous estimates in weighted variable exponent Lebesgue spaces for monotone functions for \(0 < p(x) \le q(x) < 1\). In 2020 A. Senouci and A. Zanou generalized the results of R.A. Bandaliev for quasi-monotone functions.

The aim of this paper is to obtain some generalizations of the previous results cited above for weighted Hardy operators by introducing a parameter \(\alpha \in \mathbb{R}\). Moreover, by using the quasi-norms \(\|f\|_{L^{BT}_{p(x)}(\Omega)}\) introduced by V.I. Burenkov and T.V. Tararykova, we obtain an improvement of constants in our previous estimates.

Reducibility to multiperiodic linear systems with a diagonal differentiation operator and its application to conditionally periodic systems

Zh. Sartabanov — Tue, 31 Mar 2026 00:00:00 +0000

In this paper, the main theorem is proved by establishing the reducibility to an equivalent multiperiodic linear system with a differentiation operator directed along the diagonal of the independent variables space. It is shown that helical lines on a circular cylindrical surface form periodic characteristics of the operator. The reducibility of a multiperiodic system is examined near a helix starting from the initial point of the phase circle, following the classical approach used for periodic systems.

A monodromy matrix is introduced, which remains constant along the first integrals of the characteristic equations and possesses the properties of smoothness and multiperiodicity. The existence of localised positive eigenvalues consistent with the properties of this matrix is demonstrated. It is assumed that at the initial point of the phase circle, the monodromy matrix attains the maximal number of distinct eigenvalues. Their localisation on the cylindrical surface is established using the Gershgorin method.