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The aim of this paper is to obtain new Hardy inequalities with double singular weights - at an interior point and on the boundary of the domain. These inequalities give us the possibility to derive estimates from below of the first…

Analysis of PDEs · Mathematics 2020-10-02 Nikolai Kutev , Tsviatko Rangelov

First the Hardy and Rellich inequalities are defined for the submarkovian operator associated with a local Dirichlet form. Secondly, two general conditions are derived which are sufficient to deduce the Rellich inequality from the Hardy…

Analysis of PDEs · Mathematics 2017-01-23 Derek W. Robinson

We prove multipolar Hardy inequalities on complete Riemannian manifolds, providing various curved counterparts of some Euclidean multipolar inequalities due to Cazacu and Zuazua [Improved multipolar Hardy inequalities, 2013]. We notice that…

Analysis of PDEs · Mathematics 2017-08-29 Francesca Faraci , Csaba Farkas , Alexandru Kristály

This paper is primarily devoted to a class of interpolation inequalities of Hardy and Rellich types on the Heisenberg group $\mathbb{H}^n$. Consequently, several weighted Hardy type, Heisenberg-Pauli-Weyl uncertainty principle and…

Analysis of PDEs · Mathematics 2022-09-14 Abimbola Abolarinwa , Michael Ruzhansky

Perturbations of super Poincar\'e and weak Poincar\'e inequalities for L\'evy type Dirichlet forms are studied. When the range of jumps is finite our results are natural extensions to the corresponding ones derived earlier for diffusion…

Probability · Mathematics 2015-01-27 Xin Chen , Feng-Yu Wang , Jian Wang

This paper studies the Hardy-type inequalities on the intervals (may be infinite) with two weights, either vanishing at two endpoints of the interval or having mean zero. For the first type of inequalities, in terms of new isoperimetric…

Probability · Mathematics 2012-06-25 Mu-Fa Chen

In the present paper we shall study a variational problem relating the weighted Hardy inequalities with sharp missing terms. As weights we treat non-doubling functions of the distance to the boundary of bounded domain.

Analysis of PDEs · Mathematics 2023-12-13 Hiroshi Ando , Toshio Horiuchi

This note studies the Hardy-type inequalities for vector fields with the $L^1$ norm of the $\curl$. In contrast to the well-known results in the whole space for the divergence-free vectors, we generalize the Hardy-type inequalities to the…

Analysis of PDEs · Mathematics 2014-03-18 Xingfei Xiang , Zhibing Zhang

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…

Analysis of PDEs · Mathematics 2021-03-25 J. Flynn , N. Lam , G. Lu , S. Mazumdar

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…

Functional Analysis · Mathematics 2014-06-24 Zhong-Wei Liao

We introduce a geometric approach of integral curves for functional inequalities involving directional derivatives in the general context of differentiable manifolds that are equipped with a volume form. We focus on Hardy-type inequalities…

Analysis of PDEs · Mathematics 2021-09-20 Miltiadis Paschalis

Some inequalities for different types of convexity are established.

Classical Analysis and ODEs · Mathematics 2013-09-27 Merve Avci Ardic

In this paper, we will prove several new inequalities of Hardy's types with explicit constants. The main results will be proved by making use of some generalizations of Opial's type inequalities and H\"older's inequality. To the best of the…

Classical Analysis and ODEs · Mathematics 2011-12-21 S. H. Saker

We describe propagation of torsional elastic waves in cylindrical waveguide with wedge dislocation in the framework of geometric theory of defects. The defect changes the dispersion relation. For positive deficit angles, it increases the…

Materials Science · Physics 2016-02-17 M. O. Katanaev

General Hardy-Carleman type inequalities for Dirac operators are proved. New inequalities are derived involving particular traditionally used weight functions. In particular, a version of the Agmon inequality and Treve type inequalities are…

Spectral Theory · Mathematics 2015-10-28 Alexandra Enblom

We establish various Hardy inequalities involving the distance function from submanifolds of Riemannian manifolds, where the natural weights are expressed in terms of bounds of the mean curvature of the submanifold and sectional/Ricci…

Analysis of PDEs · Mathematics 2024-01-09 Ningwei Cui , Alexandru Kristály , Wei Zhao

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.

Spectral Theory · Mathematics 2007-05-23 E B Davies

We establish a novel improvement of the classical discrete Hardy inequality, which gives the discrete version of a recent (continuous) inequality of Frank, Laptev, and Weidl. Our arguments build on certain weighted inequalities based on…

Functional Analysis · Mathematics 2024-07-09 Prasun Roychowdhury , Durvudkhan Suragan

We establish fractional Hardy-type inequalities in a bounded domain with plump complement. In particular our results apply in bounded C^\infty domains and Lipschitz domains.

Functional Analysis · Mathematics 2012-02-20 David E. Edmunds , Ritva Hurri-Syrjänen , Antti V. Vähäkangas

In this paper, we discuss the Hardy inequality with bilinear operators on general metric measure spaces. We give the characterization of weights for the bilinear Hardy inequality to hold on general metric measure spaces having polar…

Functional Analysis · Mathematics 2024-04-15 Michael Ruzhansky , Anjali Shriwastawa , Daulti Verma