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Relations between Lorentz-Zygmund and Grand Lebesgue Spaces and norms
Maria Rosaria Formica, Eugeny Ostrovsky, Leonid Sirota
We establish imbedding properties between Grand Lebesgue Spaces and (generalized) Lorentz-Zygmund ones. We extend some known previous results concerning imbedding theorems between…
Generalized Grand Lebesgue Spaces norm estimations for some operators
M. R. Formica, E. Ostrovsky, L. Sirota
We study moment rearrangement invariant spaces, which contain as particular cases the generalized Grand Lebesgue Spaces, and provide norm estimates for some operators, not necessar…
Quasilinear P.D.Es, Interpolation spaces and Hölderian mappings
Irshaad Ahmed, Alberto Fiorenza, Maria Rosaria Formica +3
As in the work of Tartar ( Tartar L. Interpolation non linéaire et régularité, 9, Journal of Functional Analysis, (1972), 469-489) we developed here some new results on non linear…
Exponential exact estimation for maximum and minimum tail of distribution for non-Gaussian random vector
M. R. Formica, E. Ostrovsky, L. Sirota
We find the exponential exact two-terms non-asymptotic expression for the maximum and minimum distribution of a non-Gaussian, in general case, random vector.
Tail estimates for random variables from interrelation between corresponding moments inequalities
M. R. Formica, E. Ostrovsky, L. Sirota
We derive the tail inequalities between two random variables starting from inequalities between its moment, or more generally between its Lebesgue-Riesz norms, which holds true on…
Weighted Grand Lebesgue Spaces norm estimation for Hardy-Sobolev-Poincare-Wirtinger operators
M. R. Formica, E. Ostrovsky, L. Sirota
We extend the classical Hardy-Sobolev-Poincare-Wirtinger inequalities from the ordinary Lebesgue-Riesz spaces into the Grand Lebesgue ones, with exact constants evaluation.
Low bounds for distribution of sums of independent centered random variables belonging to Grand Lebesgue Spaces
M. R. Formica, E. Ostrovsky, L. Sirota
We deduce in this short report the non-asymptotic for exponential tail of distribution for sums of independent centered random variables.
Modified Bernstein's inequality for sums of independent random variables
M. R. Formica, E. Ostrovsky, L. Sirota
We modify the classical Bernstein's inequality for the sums of independent centered random variables (r.v.) in the terms of relative tails or moments. We built also some examples i…
Generalization of tail inequalities for random variables, using in the martingale theory
M. R. Formica, E. Ostrovsky, L. Sirota
We generalize a famous tail Doob's inequality, relative two non-negative random variables, arising in the martingale theory, in two directions: on the more general source data and…
Moments and tail reciprocal connections for the random variables having generalized Gamma-Weibull distributions
M. R. Formica, E. Ostrovsky, L. Sirota
We establish the one-to one bilateral interrelations between an asymptotic behavior for the tail of distributions for random variables and its great moments evaluation. Our results…
Tail estimations for normed sums of centered exchangeable random variables
M. R. Formica, E. Ostrovsky, L. Sirota
We derive in this short report the exponential as well as power decreasing tail estimations for the sums of centered exchangeable random variables, alike ones for the sums of the c…
A note about extension of functions belonging to Sobolev-Grand Lebesgue Spaces
M. R. Formica, E. Ostrovsky, L. Sirota
We deduce an extension theorem for the so-called Sobolev-Grand Lebesgue Spaces defined on the suitable subsets of the whole finite-dimensional Euclidean space, and estimate the nor…
Averaging of random variables and fields
M. R. Formica, E. Ostrovsky, L. Sirota
We will prove that by averaging of random variables (r.v.) and random fields (r.f.) its tails of distributions do not increase in comparison with the tails of source variables, ess…