We obtain upper and lower estimates of the (p; q) norm of the convolution operator. The upper estimate sharpens the Young-type inequalities due to O'Neil and Stepanov.

We study norm convolution inequalities in Lebesgue and Lorentz spaces. First, we improve the well-known O’Neil’s inequality for the convolution operators and prove corresponding estimate from below. Second, we obtain ...

We study norm convolution inequalities in Lebesgue and Lorentz spaces. First, we improve the well-known O’Neil’s inequality for the convolution operators and prove corresponding estimate from below. Second, we obtain ...

The Einstein equation for the Friedmann-Robertson-Walker metric plays a fundamental role in cosmology. The direct search of the exact solutions of the Einstein equation even in this simple metric case is sometime a hard ...

The vortex filament equations (VFE) in 1+1 and 2+1 dimensions are considered. Some of these equations are integrable. Also the VFE with potentials and with selfconsistent potentials are presented. Finally several examples ...

The purpose of this note is to consider the relationship of some multidimensional spaces and some partial differential equations (PDE). The study of the deep relationship between differential geometry and PDE has a long ...

The discovery of a damage-resistant alloy based on Hf solute additions to a low-carbon 316SS is the highlight of the Phase 2 research. This damage resistance is supported by characterization of radiation-induced ...

Astana: L.N. Gumilyov Eurasian National University, 2010. Single LiF crystals were irradiated with Xe (195 MeV), Kr (117 MeV), and N (18 MeV) ions. Using absorption spectroscopy, color center creation was analyzed as a ...

In article considered the problem of curved rod fluctuation with JungB (TM) s module. Shown the civility of the problem formulation. For solution used integro - interpolation method. Constructed implicit differential scheme, ...