相关论文: Covariation inequality in Grand Lebesgue Spaces
We study moment rearrangement invariant spaces, which contain as particular cases the generalized Grand Lebesgue Spaces, and provide norm estimates for some operators, not necessarily linear, acting between some measurable rearrangement…
In this paper, the problem of reconstruction of signals in mixed Lebesgue spaces from their random average samples has been studied. Probabilistic sampling inequalities for certain subsets of shift-invariant spaces have been derived. It is…
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…
Estimation of the mean vector and covariance matrix is of central importance in the analysis of multivariate data. In the framework of generalized linear models, usually the variances are certain functions of the means with the normal…
In this short paper we generalize the classical inequality between the norms in Lebesgue spaces of the functions and its derivatives, which in the multidimensional case are called Sobolev's inequalities, on the many popular classes pairs of…
This paper considers a multivariate spatial random field, with each component having univariate marginal distributions of the skew-Gaussian type. We assume that the field is defined spatially on the unit sphere embedded in $\mathbb{R}^3$,…
In this manuscript we consider random objects being measured in multiple metric spaces, which may arise when those objects may be measured in multiple distinct ways. In this new multivariate setting, we define a Fr\'echet covariance and…
Solutions of the bivariate, linear errors-in-variables estimation problem with unspecified errors are expected to be invariant under interchange and scaling of the coordinates. The appealing model of normally distributed true values and…
A possibility to represent the standard model of fundamental particles covariant derivatives by means of approximate generalized fractional Riemann-Liouville derivatives of multifractal time and space model is shown.
In a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we show that functions of bounded variation (BV functions) can be approximated in the strict sense and pointwise uniformly by special…
We calculate the so-called Rademacher's Grand Lebesgue Space norm for a centered (shifted) indicator (Bernoulli's, binary) random variable. This norm is optimal for the centered and bounded random variables (r.v.). Using this result we…
We study inequalities of the form \begin{equation*} \rho ( \lvert \hat{f} \rvert) \leq C \sigma(f) < \infty, \end{equation*} with $f \in L_{1}(\mathbb{R}^n)$, the Lebesgue-integrable functions on $\mathbb{R}^n$ and \begin{equation*}…
We characterize the rearrangement-invariant hull, with respect to a given measure $\mu$, of weighted Lebesgue spaces. The solution leads us to first consider when this space is contained in the sum of $(L^1 + L^\infty)(R, \mu)$ and the…
In this work, we consider the problem of bounding the values of a covariance function corresponding to a continuous-time stationary stochastic process or signal. Specifically, for two signals whose covariance functions agree on a finite…
In this paper we study the problem of estimating the alpha-, beta- and phi-mixing coefficients between two random variables, that can either assume values in a finite set or the set of real numbers. In either case, explicit closed-form…
Finding the eigenvalues connected to the covariance operator of a centred Hilbert-space valued Gaussian process is genuinely considered a hard problem in several mathematical disciplines. In statistics this problem arises for instance in…
This paper starts by introducing results from geometric measure theory to prove symmetric decreasing rearrangement inequalities on $\mathbb{R}^n$, which give multiple proofs of the isoperimetric and P\'{o}lya-Szeg\H{o} inequalities. Then we…
In this work the Isoperimetric Inequality for integral varifolds is used to obtain sharp estimates for the size of the set where the density quotient is small and to generalise Calder\'on's and Zygmund's theory of first order…
In this short article we show a particular version of the Hedberg inequality which can be used to derive, in a very simple manner, functional inequalities involving Sobolev and Besov spaces in the general setting of Lebesgue spaces of…
Multivariate generalized Gamma convolutions are distributions defined by a convolutional semi-parametric structure. Their flexible dependence structures, the marginal possibilities and their useful convolutional expression make them…