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Leonid Sirota

Publications and source records attributed to Leonid Sirota.

At least 19 recordsLinked to original sources
arXiv2026

Estimates for tail functions under Riesz transforms in Grand Lebesgue Spaces

We study the tail behaviour of measurable functions under generalized Riesz-type operators in the framework of Grand Lebesgue Spaces. By exploiting the connection between the growth of $L^p$ norms and the Young--Fenchel transform, we derive explicit tail estimates from suitable $L^p$ bounds. We also present model examples and apply the abstract result to the classical Riesz transforms, showing how the $L^p$ growth of the operator interacts with the intrinsic tail behaviour of the input function.

math.FA↗
arXiv2024

Moment and exponential estimation for the distribution of the norms for random matrices martingales

We derive sharp non - asymptotical Lebesgue - Riesz as well as Grand Lebesgue Space norm estimations for different norms of matrix martingales through these norms for the correspondent martingale differences and through the entropic dimension of the extremal points of the unit ball for a basic space. These estimates allow us to deduce in particular the exponential decreasing tail of distribution for these norms of matrix martingales. We bring also some examples in order to show the exactness of the obtained estimations.

math.PR↗
arXiv2024

Factorizable convergence of random variables in Grand Lebesgue Spaces

We obtain results concerning the so-called factorization for the convergence of random variables almost everywhere (almost surely or with probability one), belonging to the classical Lebesgue-Riesz spaces and we extend these results to the Grand Lebesgue Spaces. We also give exact estimates for the parameters involved and provide several examples. We also show that the obtained estimates are, in the general case, essentially non-improvable, of course up to a multiplicative constant.

math.PR↗
arXiv2022

Relations between Lorentz-Zygmund and Grand Lebesgue Spaces and norms

We establish imbedding properties between Grand Lebesgue Spaces and (generalized) Lorentz-Zygmund ones. We extend some known previous results concerning imbedding theorems between Grand Lebesgue and classical Lebesgue-Riesz spaces and we show the exactness of the obtained estimates.

math.FA↗
arXiv2020

Gaussian and non-Gaussian distributed random analytical and entire functions

We investigate the complex Gaussian as well as non-Gaussian distributed random analytical and entire functions (complex entire random field) and calculate their domain of definiteness (radius of convergence) as well as some important characteristics: order and type. As a consequence we deduce that all the mentioned characteristics, under very natural conditions, are deterministic (non-random) with probability one and we calculate them. Moreover we exhibit some examples to show the exactness of the obtained results.

math.CV↗
arXiv2020

Quasi Grand Lebesgue Spaces

We introduce a new class of quasi-Banach spaces as an extension of the classical Grand Lebesgue Spaces for small values of the parameter, and we investigate some its properties, in particular, completeness, fundamental function, operators estimates, Boyd indices, contraction principle, tail behavior, dual space, generalized triangle and quadrilateral constants and inequalities.

math.FA↗
arXiv2020

Bochner-Riesz operators in Grand Lebesgue spaces

We provide the conditions for the boundedness of the Bochner-Riesz operator acting between two different Grand Lebesgue Spaces. Moreover we obtain a lower estimate for the constant appearing in the Lebesgue-Riesz norm estimation of the Bochner-Riesz operator and we investigate the convergence of the Bochner-Riesz approximation in Lebesgue-Riesz spaces.

math.FA↗
arXiv2019

Fundamental solution for Cauchy initial value problem for parabolic PDEs with discontinuous unbounded first-order coefficient at the origin. Extension of the classical parametrix method

We prove the existence of a fundamental solution of the Cauchy initial boundary value problem on the whole space for a parabolic partial differential equation with discontinuous unbounded first-order coefficient at the origin. We establish also non-asymptotic, rapidly decreasing at infinity, upper and lower estimates for the fundamental solution. We extend the classical parametrix method provided by E.E. Levi.

math.AP↗
arXiv2016

Discovering of boundedness and continuity of random fields by means of partition entropic scheme

We construct a new sufficient conditions for boundedness or continuity of arbitrary random fields relying on the so-called partition scheme, alike in the classical majorizing measure method. We deduce also the used in the practice (statistics, method Monte-Carlo etc.) exact exponential estimates for tail of distribution of maximum for random field satisfying formulated in this report conditions.

math.PR↗