相关论文: Hardy-type Inequalities Via Auxiliary Sequences

In this paper we present many congruences for several Ap\'ery-like sequences.

We illustrate the interplay between certain discrete and continuous problems, by presenting a method for the study of the asymptotics of a divergent sequence, through consideration of the asymptotics of its continuous analogue

Number sequences defined by a linear recursion relation are studied by means of generating functions. Indices of the terms in the recursion relation have arbitrary differenses. In addition to formulas for the nth term an algorithm is…

We extend a result of Levin and Ste\v{c}kin concerning an inequality analogous to Hardy's inequality.

In this paper, nonstandard multistep methods are considered. It is shown that under some (sufficient and necessary) conditions, these methods attain the same order as their standard counterparts - to prove this statement, a nonstandard…

In this paper, we present the geometric Hardy inequalities on the starshaped sets in the Carnot groups. Also, we obtain the geometric Hardy inequalities on half-spaces for general vector fields.

In this work, we consider weighted anisotropic Hardy inequalities and trace Hardy inequalities involving a general Finsler metric. We follow a unifying approach, by establishing first a sharp interpolation between them, extending the…

We prove certain generalization of Hardy's inequality where the "boundary defining function" is replaced by a polynomial defining a singular algebraic variety. An application is given on the existence of a small time heat trace expansion…

In this paper we present a unified simple approach to anisotropic Hardy inequalities in various settings. We consider Hardy inequalities which involve a Finsler distance from a point or from the boundary of a domain. The sharpness and the…

In the present paper we shall establish n-dimensional Hardy's inequalities with non-doubling weight functions of the distance to the boundary, where the boundary is a $C^2$ class bounded domain of $R^N$. This work is essentially based on…

Certain rearrangement inequalities of a type considered by Hardy, Riesz, and Brascamp-Lieb-Luttinger are studied. Subsets of the real line that extremize these inequalities are characterized. Our results apply only to special cases, and…

We define a proper differential sequence of ordinary differential equations and introduce a method to derive an alternative sequence of integrals for such a sequence. We describe some general properties which are illustrated by several…

In this paper we give a version of Harris' criterion for determining $H^{1,p}_0$ within $H^{1,p}$ on discrete spaces. Moreover, we provide a converse via Hardy inequalities involving distances to metric boundaries.

We prove a general inequality for more than two sequences mirroring that of the discrete two-sequence Cauchy-Schwarz.

Some inequalities for different types of convexity are established.

We establish a family of parametric isoperimetric-type inequalities with multiple geometric quantities for closed convex curves. These inequalities hold under certain parameter conditions. We also prove the equality conditions. Some new…

The joint ergodicity classification problem aims to characterize those sequences which are jointly ergodic along an arbitrary dynamical system if and only if they satisfy two natural, simpler-to-verify conditions on this system. These two…

We prove thin-thick decompositions, for the class of Hardy martingales and thereby strengthen its square function characterization. We apply the underlying method to several classical martingale inequalities, for which we give new proofs .

The current status concerning Hardy-type inequalities with sharp constants is presented and described in a unified convexity way. In particular, it is then natural to replace the Lebesgue measure $dx$ with the Haar measure $dx/x.$ There are…

In this paper we study the extension problem for the sublaplacian on a $H$-type group and use the solutions to prove trace Hardy and Hardy inequalities for fractional powers of the sublaplacian.