A Remark on the Inequalities of Bernstein - Markov Type in Exponential Orlicz and Lorentz Spaces

We prove in this article the generalizations on the exponential Orlicz spaces Markov's - Bernstein's inequalities for algebraic polynomials and rational functions.Comment: 14 page

Strichartz type Inequalities for Parabolic and Schr\"odinger Equations in rearrangement invariant Spaces

In this paper we generalize the classical Strichartz estimation for solutions of initial problem for linear parabolic and Schr\"odinger PDE on many popular classes {\it pairs} of rearrangement invariant(r.i.) spaces and construct some examples in order to show the exactness of our estimations

Non-asymptotical sharp exponential estimates for maximum distribution of discontinuous random fields

We offer in this paper the non-asymptotical bilateral sharp exponential estimates for tail of maximum distribution of {\it discontinuous} random fields. Our consideration based on the theory of Prokhorov-Skorokhod spaces of random fields and on the theory of multivariate Banach spaces of random variables with exponential decreasing tails of distributions.Comment: arXiv admin note: substantial text overlap with arXiv:1510.0418

Monte-Carlo method for multiple parametric integrals calculation and solving of linear integral Fredholm equations of a second kind, with confidence regions in uniform norm

In this article we offer some modification of Monte-Carlo method for multiple parametric integral computation and solving of a linear integral Fredholm equation of a second kind (well posed problem). We prove that the rate of convergence of offered method is optimal under natural conditions still in the uniform norm, and construct an asymptotical and non-asymptotical confidence region, again in the uniform norm

Necessary Conditions for Fractional Hardy-Sobolev's Inequalities

In this short article we obtain some necessary conditions for a so-called fractional Hardy-Sobolev's inequalities in multidimensional case. We also give some examples to show the sharpness of these inequalities

Weighted Hardy-Littlewood average operators on bilateral grand Lebesgue spaces

We obtain in this short article the non-asymptotic exact estimations for the norm of (generalized) weighted Hardy-Littlewood average integral operator in the so-called Bilateral Grand Lebesgue Spaces. We also give examples to show the sharpness of these inequalities

Lebesgue-Riesz norm estimates for fractional Laplace transform

We obtain in this short article the bilateral non-asymptotic estimations for the norm in Lebesgue-Riesz and bilateral Grand Lebesgue spaces of the so-called fractional Laplace integral transform. We give also examples to show the sharpness of these inequalities

Non-asymptotic estimation for Bell function, with probabilistic applications

We deduce the non-asymptotical bilateral estimates for moment inequalities for sums of non-negative independent random variables, based on the correspondent estimates for the so-called Bell functions and the Poisson distribution

Weight Hardy-Littlewood Inequalities for Different Powers

In this short article we obtain the non-asymptotic upper and low estimations for linear and bilinear weight Riesz's functional through the Lebesgue spaces

Central Limit Theorem and exponential tail estimations in mixed (anisotropic) Lebesgue spaces

We study the Central Limit Theorem (CLT) in the so-called mixed (anisotropic) Lebesgue-Riesz spaces and tail behavior of normed sums of centered random independent variables (vectors) with values in these spaces