Related papers: An Extension of Young's Inequality
We give a refined Young inequality which generalizes the inequality by Zou--Jiang. We also show the upper bound for the logarithmic mean by the use of the weighted geometric mean and the weighted arithmetic mean. Furthermore, we show some…
Multilinear trace restriction inequalities are obtained for Hardy's inequality. More generally, detailed development is given for new multilinear forms for Young's convolution inequality, and a new proof for the multilinear…
We provide explicit sufficient conditions for absolute continuity and equivalence between the distributions of two jump-diffusion processes that can explode and be killed by a potential.
Measurement professionals cannot come to an agreement on the definition of the term 'item fairness'. In this paper a continuous measure of item unfairness is proposed. The more the unfairness measure deviates from zero, the less fair the…
A generalization of the H\"older inequality is considered. Its relations with a previously obtained improvement of the Cauchy--Schwarz inequality are discussed.
In this note we present a version of Hardy's inequality on a measure space $(X,\mu)$ endowed with a measurable function $N\colon X\to \mathbb R$ which replaces the absolute value on $\mathbb R$ or $\mathbb R^n$, and, more generally, the…
We combine continuous and integral logics and found a logical framework for metric measure spaces equipped with a family of continuous relations and operations. We prove the ultraproduct theorem and deduce compactness and other usual…
In this technical note, we give two extensions of the classical Fano inequality in information theory. The first extends Fano's inequality to the setting of estimation, providing lower bounds on the probability that an estimator of a…
Hypercontractive inequalities are a useful tool in dealing with extremal questions in the geometry of high-dimensional discrete and continuous spaces. In this survey we trace a few connections between different manifestations of…
We present new counterexamples, which provide stronger limitations to sums-differences statements than were previously known. The main idea is to consider non-uniform probability measures.
In this paper, we extend the investigations regarding Birkhoff-James orthogonality of linear operators to bounded continuous functions on metric spaces. We introduce Birkhoff-James extensions of continuous functions and study them in…
A classical inequality, which is known for families of monotone functions, is generalized to a larger class of families of measurable functions. Moreover we characterize all the families of functions for which the equality holds. We apply…
We study generalized means whose domain may contain unbounded sets as well. We investigate usual properties of this type of means and also new attributes that regard for such means only. We examine how a mean defined on bounded sets can be…
Finite metric spaces are the object of study in many data analysis problems. We examine the concept of weak isometry between finite metric spaces, in order to analyse properties of the spaces that are invariant under strictly increasing…
We give a new proof of the sharp form of Young's inequality for convolutions, first proved by Beckner [Be] and Brascamp-Lieb [BL]. The latter also proved a sharp reverse inequality in the case of exponents less than $1$. Our proof is…
A stability version of the reverse isoperimetric inequality, and the corresponding inequality for isotropic measures are established.
We extend the definition of weak symmetric continuity to be applicable for functions defined on any nonempty subset of $\R$. Then we investigate basic properties of weakly symmetrically continuous functions and compare them with those of…
We show that the intuitionistic first-order theory of equality has continuum many complete extensions. We also study the Vitali equivalence relation and show there are many intuitionistically precise versions of it.
We give the definition of uniform symmetric continuity for functions defined on a nonempty subset of the real line. Then we investigate the properties of uniformly symmetrically continuous functions and compare them with those of…
With a new proof approach we prove in a more general setting the classical convergence theorem that almost everywhere convergence of measurable functions on a finite measure space implies convergence in measure. Specifically, we generalize…