相关论文: The Bennett-Orlicz norm

We introduce two uncertainty relations based on the state-dependent norm of commutators, utilizing generalizations of the B\"ottcher-Wenzel inequality. The first relation is mathematically proven, while the second, tighter relation is…

We give a new approach, inspired by H\"ormander's $L^2$-method, to weighted variance inequalities which extend results obtained by Bobkov and Ledoux. It provides in particular a local proof of the dimensional functional forms of the…

In this paper we first extend a generalization of Ostrowski type inequality on time scales for functions whose derivatives are bounded and then unify corresponding continuous and discrete versions. We also point out some particular integral…

We develop a class of exponential bounds for the probability that a martingale sequence crosses a time-dependent linear threshold. Our key insight is that it is both natural and fruitful to formulate exponential concentration inequalities…

The sliding window model generalizes the standard streaming model and often performs better in applications where recent data is more important or more accurate than data that arrived prior to a certain time. We study the problem of…

We provide necessary and sufficient conditions for the coincidence, up to equivalence of the norms, between strong and weak Orlicz spaces. Roughly speaking, this coincidence holds true only for the so-called exponential spaces. We find also…

A comprehensive analysis of Sobolev-type inequalities for the Ornstein-Uhlenbeck operator in the Gauss space is offered. A unified approach is proposed, providing one with criteria for their validity in the class of rearrangement-invariant…

Lutwak's notion of affine quermassintegrals of a convex body quickly became of great importance in convex and affine geometry and more recently, also in asymptotic geometric analysis. In this note we introduce the notion of Orlicz mixed…

We define the notion of Bernstein measures and Bernstein approximations over general convex polytopes. This generalizes well-known Bernstein polynomials which are used to prove the Weierstrass approximation theorem on one dimensional…

In this paper we present new versions of the classical Brunn-Minkowski inequality for different classes of measures and sets. We show that the inequality \[ \mu(\lambda A + (1-\lambda)B)^{1/n} \geq \lambda \mu(A)^{1/n} +…

Inspired by the work of Cordero-Erausquin, McCann and Schmuckenschl\"ager [{\it Invent. Math.,} 2001], we derive an explicit expression for the Jacobian determinant of the normal exponential map on a submanifold, establishing a relationship…

This paper is devoted to improvements of Sobolev and Onofri inequalities. The additional terms involve the dual counterparts, i.e. Hardy-Littlewood-Sobolev type inequalities. The Onofri inequality is achieved as a limit case of Sobolev type…

We obtain some sufficient conditions for the Central Limit Theorem for the random processes (fields) with values in the separable part of Holder space in the modern terms of majorizing (minorizing) measures, belonging to X.Fernique and…

We present an abstract form of the Pr\'ekopa-Leindler inequality that includes several known -and a few new- related functional inequalities on Euclidean spaces. The method of proof and also the formulation of the new inequalities are based…

The main study of this article is the characterization of Richard's inequality, because it is closely related to Buzano's inequality. Finally, we present a newapproach for Richard's inequality, where we use the Selberg operator.

Bernstein inequalities and inverse theorems are a recent development in the theory of radial basis function(RBF) approximation. The purpose of this paper is to extend what is known by deriving $L^p$ Bernstein inequalities for RBF networks…

Central limit theorems (CLTs) for high-dimensional random vectors with dimension possibly growing with the sample size have received a lot of attention in the recent times. Chernozhukov et al. (2017) proved a Berry--Esseen type result for…

We study Bell's inequality in relation to the Einstein-Podolsky-Rosen paradox in the relativistic regime. For this purpose, a relativistically invariant observable is used in the calculation of the Bell's inequality, which results in the…

Orlicz spaces are generalizations of Lebesgue spaces. The sufficient and necessary conditions for generalized H\"{o}lder's inequality in Lebesgue spaces and in weak Lebesgue spaces are well known. The aim of this paper is to present…

A plethora of spaces in Functional Analysis (Braun-Meise-Taylor and Carleman ultradifferentiable and ultraholomorphic classes; Orlicz, Besov, Lipschitz, Lebesque spaces, to cite the main ones) are defined by means of a weighted structure,…