On Some Properties of Convolutions in Variable Exponent Lebesgue Spaces

A convolution in the variable exponent Lebesgue spaces \(L_{2\pi }^{p\left( \cdot \right) }\) is defined and its basic properties are investigated. It is also proved that this convolution can be approximated in \(L_{2\pi }^{p\left( \cdot \right) }\) by the finite linear combinations of Steklov means of the original function.     

Stress state of saturated viscoelastic masses with cylindrical workings

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 25, No. 2, pp. 76–82, February, 1989.     

Linearization of dynamic equations for a saturated porous medium

Equations of the mechanics of a saturated porous medium that account for the deformation tensor of the fluid and the initial state of the medium are derived. Emphasis is on the linearization and justification of the basic nonlinear equations of the theory. The relationship between the pressure (deformation) of the fluid and the thermodynamic and kinematic parameters of the medium is established. The solutions obtained are compared with Biot’s well-known classical results and analyzed     

Approximation in weighted Smirnov classes

In this work, the direct and inverse problems of approximation theory in the weighted Smirnov classes of analytic functions defined on the domains with a regular boundary are investigated. In particular, the constructive characterization of the generalized Lipschitz classes of functions are obtained.     

On approximation in Weighted Orlicz spaces

An inverse theorem of the trigonometric approximation theory in Weighted Orlicz spaces is proved and the constructive characterization of the generalized Lipschitz classes defined in these spaces is obtained.