Related papers: Grand Lebesgue Spaces norm estimates for multivari…

Transcendental functions, such as exponentials and logarithms, appear in a broad array of computational domains: from simulations in curvilinear coordinates, to interpolation, to machine learning. Unfortunately they are typically expensive…

This paper presents a general study of one-dimensional differentiability for functionals defined on convex domains that are not necessarily open. The local approximation is carried out using affine functionals, as opposed to linear…

We obtain in this paper a non-asymptotic non-improvable up to multiplicative constant moment and exponential tail estimates for distribution for U-statistics by means of martingale representation. We show also the exactness of obtained…

In this paper, we review recent results on stability and instability in logarithmic Sobolev inequalities, with a particular emphasis on strong norms. We consider several versions of these inequalities on the Euclidean space, for the…

In this article we prove weighted norm inequalities and pointwise estimates between the multilinear fractional integral operator and the multilinear fractional maximal. As a consequence of these estimations we obtain weighted weak and…

We give a general method to obtain from the integral restrictions of functions sharp pointwise and uniform estimates of these functions. This scheme is illustrated by the examples for Fock\,--\,Bargmann spaces of entire functions of several…

We prove some Sawyer-type characterizations for multilinear fractional maximal function for the upper triangle case. We also provide some two-weight norm estimates for this operator. As one of the main tools, we use an extension of the…

We bring in this short report (counter -) examples on order to show a difference between tails behavior and Grand Lebesgue Spaces norms for some classes of random variables.

In this paper we investigate the question of estimating the Gram operator by a robust estimator from an i.i.d. sample in a separable Hilbert space and we present uniform bounds that hold under weak moment assumptions. The approach consists…

Very large spatio-temporal lattice data are becoming increasingly common across a variety of disciplines. However, estimating interdependence across space and time in large areal datasets remains challenging, as existing approaches are…

We establish generalized Gaussian bounds and local limit theorems with Gaussian-type error for the convolution powers of certain complex-valued functions on $\mathbb{Z}^d$. These global space-times estimates/error, which are sharp in…

We consider the notion of the matrix (tensor) distribution of a measurable function of several variables. On the one hand, it is an invariant of this function with respect to a certain group of transformations of variables; on the other…

In this paper, we prove some uniform estimates between Lebesgue and Hardy spaces for operators closely related to the multilinear paraproducts on R^d. We are looking for uniformity with respect to parameters, which allow us to disturb the…

The classical $L^2$ estimate for the $\overline{\partial}$ operators is a basic tool in complex analysis of several variables. Naturally, it is expected to extend this estimate to infinite dimensional complex analysis, but this is a…

We give a necessary and sufficient condition for non-local functionals on vector-valued Lebesgue spaces to be weakly sequentially lower semi-continuous. Here a non-local functional shall have the form of a double integral of a density which…

We establish sharp tail asymptotics for component-wise extreme values of bivariate Gaussian random vectors with arbitrary correlation between the components. We consider two scaling regimes for the tail event in which we demonstrate the…

Let $\bx_j = \btheta +\bep_j, j=1,...,n$, be observations of an unknown parameter $\btheta$ in a Euclidean or separable Hilbert space $\scrH$, where $\bep_j$ are noises as random elements in $\scrH$ from a general distribution. We study the…

The problem of estimating a linear functional based on observational data is canonical in both the causal inference and bandit literatures. We analyze a broad class of two-stage procedures that first estimate the treatment effect function,…

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…

A new class of bivariate poly-analytic Hermite polynomials is considered. We show that they are realizable as the Fourier-Wigner transform of the univariate complex Hermite functions and form a nontrivial orthogonal basis of the classical…