let = be a non-negative matrix. denote by the supremum of those , satisfying the following inequality: where , , and also is increasing, non-negative sequence of real numbers. if we used instead of the purpose of this paper is to establish a hardy type formula for , where is hausdorff matrix and a similar result is also established for where in particular, we apply our results to the cesaro...

We describe some elements of the theory of semigroups generated by second order differential operators needed to study the Hardy-type space H1 L related to the time independent Schrödinger operator L = −∆+ V , with V ≥ 0 a potential satisfying a reverse Hölder inequality. Its dual space is a BMO-type space BMOL, that turns out to be the suitable one for the versions of some classical operators ...

We determine the sharp constant in the Hardy inequality for fractional Sobolev spaces. To do so, we develop a non-linear and non-local version of the ground state representation, which even yields a remainder term. From the sharp Hardy inequality we deduce the sharp constant in a Sobolev embedding which is optimal in the Lorentz scale. In the appendix, we characterize the cases of equality in t...

In this paper, we study the asymptotic behaviour of sharp constant in discrete Hardy and Rellich inequality on lattice $\mathbb{Z}^d$ as $d \rightarrow \infty$. process, proved some Hardy-type inequalities for operators $\Delta^m$ $\nabla(\Delta^m)$ non-negative integers $m$ a $d$ dimensional torus. It turns out that grows $d^2$ respectively $ d

We review the literature concerning the Hardy inequality for regions in Euclidean space and in manifolds, concentrating on the best constants. We also give applications of these inequalities to boundary decay and spectral approximation. AMS subject classifications: 35P99, 35P20, 47A75, 47B25 keywords: Hardy inequality, boundary decay, Laplacian, elliptic operators, spectral theory, eigenfunctio...

By using an alternative, equivalent form of the CHSH inequality and making extensive use of the experimentally testable property of physical locality we determine the 64 different Bell-type inequalities (each one involving four joint probabilities) into which Hardy’s nonlocality theorem can be cast. This allows one to identify all the two-qubit correlations which can exhibit Hardy-type nonlocal...