相关论文: On the Bombieri Inequality in Inner Product Spaces

In this paper we study the problem of deriving further Sobolev inequalities from a given Sobolev inequality. We use several different methods, including Bessel potentials and Riesz transforms. We apply the results to the Ricci flow to…

The derivation of Bell inequalities in terms of quantum statistical (thermodynamic) entropies is considered. Inequalities of the Wigner form are derived but shown to be extremely limiting in their applicability due to the nature of the…

We develop a theory of bounded variation functions and Besov spaces in abstract Dirichlet spaces which unifies several known examples and applies to new situations, including fractals.

The algebraic derivation of the numerical limits of Bell inequalities in either three or four random variables is independent of the assumption of randomness.The limits of the inequalities follow as mathematical consequences of their…

A natural link between the notions of majorization and strongly Sperner posets is elucidated. It is then used to obtain a variety of consequences, including new R\'enyi entropy inequalities for sums of independent, integer-valued random…

The sharp constants in a family of exponential Sobolev type inequalities in Gauss space are exhibited. They constitute the Gaussian analogues of the Moser inequality in the borderline case of the Sobolev embedding in the Euclidean space.…

In this paper we derive a new class of sum rules for products of the Bessel functions of first kind. Using standard algebraic manipulations we extend some of the well known properties of $J_n$. Some physical applications of the results are…

Bessel potential spaces, introduced in the 1960s, are derived through complex interpolation between Lebesgue and Sobolev spaces, making them intermediate spaces of fractional differentiability order. Bessel potential spaces have recently…

The aim of this article is to give some improvements of Jordan-Steckin and Becker-Stark inequalities discussed in [1].

We review several inequalities concerning Gaussian measures - isoperimetric inequality, Ehrhard's inequality, Bobkov's inequality, S-inequality and correlation conjecture.

The present paper is devoted to the study of Jensen-Mercer-type inequalities. Our results generalize and improve some earlier results in the literature.

We prove new versions of the isomorphic Busemann-Petty problem for two different measures and show how these results can be used to recover slicing and distance inequalities. We also prove a sharp upper estimate for the outer volume ratio…

A direct approach to Ball's simplex inequality is presented. This approach, which does not use the Brascamp-Lieb inequality, also gives Barthe's characterization of the simplex for Ball's inequality and extends it from discrete to arbitrary…

If $P$ is an orthogonal projection defined on an inner product space $\mathcal{H}$, then the inequality $$ |\langle Px, y\rangle|\leq \frac12 [\|x\|\|y\|+|\langle x, y\rangle|] $$ fulfills for any $x,y \in \mathcal{H}$ (see \cite{Dra16}).…

This paper announces the discovery of an isoperimetric inequality for the area of plane regions defined by binary forms. This result has been applied subsequently in the enumeration of solutions to the Thue inequality and, given its…

The main aim of this paper is to prove a generalization of the classical Bohr theorem and as an application, we obtain a counterpart of Bohr theorem for the generalized Ces\'aro operator.

Our main purpose is to establish Gagliardo-Nirenberg type inequalities using fractional homogeneous Sobolev spaces, and homogeneous Besov spaces. In particular, we extend some of the results obtained by the authors in [1, 2, 3, 7, 16, 21].

We recognise that an entropy inequality akin to the main intermediate goal of recent works (Gowers, Green, Manners, Tao [3],[2]) regarding a conjecture of Marton provides a black box from which we can also through a short deduction recover…

We give a distribution-dependent concentration inequality for functions of independent variables. The result extends Bernstein's inequality from sums to more general functions, whose variation in any argument does not depend too much on the…

We study the Hardy identities and inequalities on Cartan-Hadamard manifolds using the notion of a Bessel pair. These Hardy identities offer significantly more information on the existence/nonexistence of the extremal functions of the Hardy…