Related papers: An improved discrete Hardy inequality
To estimate the optimal constant in Hardy-type inequalities, some variational formulas and approximating procedures are introduced. The known basic estimates are improved considerably. The results are illustrated by typical examples. It is…
A refinement of the Hardy inequality has been presented by use of superquadratic function.
Based on a new idea of factorization, we prove an improved discrete Rellich inequality and discuss its optimality. We also give a conjecture on improved higher order discrete Hardy-like inequalities and formulate an open problem for the…
This is a chapter from PhD Thesis by Stefano Biagi (advisor: prof. A. Bonfiglioli). We overview existing results showing that it is possible to generalize the classical Hardy's Inequality to more general linear partial differential…
In this current work, we revisit the recent improvement of the discrete Hardy's inequality in one dimension and establish an extended improved discrete Hardy's inequality with its optimality. We also study one-dimensional discrete Copson's…
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…
We consider a multidimensional version of an inequality due to Leray as a substitute for Hardy's inequality in the case $p=n\geq2.$ In this paper we provide an optimal Sobolev-type improvement of this substitute, analogous to the…
This paper studies the Hardy-type inequalities on the discrete intervals. The first result is the variational formulas of the optimal constants. Using these formulas, one may obtain an approximating procedure and the known basic estimates…
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 give a~new proof of the known criteria for the inequality \begin{equation*} \left(\int_{0}^{\infty}\left(\int_{0}^{t}f\right)^{q}w(t)\,dt\right)^{\frac{1}{q}} \leq C \left(\int_{0}^{\infty}f^{p}v\right)^{\frac{1}{p}}. \end{equation*} The…
We establish an analog Hardy inequality with sharp constant involving exponential weight function. The special case of this inequality (for n=2) leads to a direct proof of Onofri inequality on S^2.
The Hardy Inequality (HI) for potentials with countably many singularities of the form $V=\sum_{k\in \mathbf{Z}}\frac{1}{|x-a_k|^2}$ is not a trivial issue. In principle, the more singular poles are, the less the Hardy constant is: it is…
We present a unified approach to improved $L^p$ Hardy inequalities in $\R^N$. We consider Hardy potentials that involve either the distance from a point, or the distance from the boundary, or even the intermediate case where distance is…
We extend Hardy's inequality from sequences of non-negative numbers to sequences of positive semi-definite operators if the parameter p satisfies 1<p<=2, and to operators under a trace for arbitrary p>1. Applications to trace functions are…
Using recent results concerning the homogenization and the Hardy property of weighted means, we establish sharp Hardy constants for concave and monotone weighted quasideviation means and for a few particular subclasses of this broad family.…
In this note we produce generalized versions of the classical inequalities of Hardy and of Hilbert and we establish their equivalence. Our methods rely on the H^1-BMOA duality. We produce a class of examples to establish that the…
We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the Aharonov-Bohm field in all dimensions and establish a sharp Hardy-type inequality that takes…
We prove a sharp integral inequality that generalizes the well known Hardy type integral inequality for negative exponents. We also give sharp applications in two directions for Muckenhoupt weights on R. This work refines the results that…
We study Hardy inequalities for antisymmetric functions in three different settings: euclidean space, torus and the integer lattice. In particular, we show that under the antisymmetric condition the sharp constant in Hardy inequality…
In the present paper we shall improve one dimensional weighted Hardy inequalities with one-sided boundary condition by adding sharp remainders. As an application, we shall establish n dimensional weighted Hardy inequalities in a bounded…