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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.

Functional Analysis · Mathematics 2023-03-14 Simon Murmann , Marcel Schmidt

Some trapezoid and mid-point type inequalities related to the Hermite-Hadamard inequality for the mappings defined on a ball in the space are obtained.

General Mathematics · Mathematics 2019-05-28 M. Rostamian Delavar

We obtain new variants of weighted Gagliardo-Nirenberg interpolation inequalities in Orlicz spaces, as a consequence of weighted Hardy-type inequalities. The weights we consider need not be doubling.

Functional Analysis · Mathematics 2009-11-02 Agnieszka Kalamajska , Katarzyna Pietruska-Paluba

We prove a sharp Hardy inequality for fractional integrals for functions that are supported on a general domain. The constant is the same as the one for the half-space and hence our result settles a recent conjecture of Bogdan and Dyda.

Analysis of PDEs · Mathematics 2010-02-22 Michael Loss , Craig Sloane

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 use different approaches to study a generalization of a result of Levin and Ste\v{c}kin concerning an inequality analogous to Hardy's inequality. Our results lead naturally to the study of weighted remainder form of Hardy-type…

Functional Analysis · Mathematics 2009-07-31 Peng Gao

We prove a fractional Hardy-type inequality for vector fields over the half space based on a modified fractional semi-norm. A priori, the modified semi-norm is not known to be equivalent to the standard fractional semi-norm and in fact…

Functional Analysis · Mathematics 2018-08-08 Tadele Mengesha

In this article, we give a short proof of Hardy's inequality for Hermite expansions of functions in the classical Hardy spaces $H^p({\mathbb R^n})$, by using an atomic decomposition of the Hardy spaces associated with the Hermite operators.…

Classical Analysis and ODEs · Mathematics 2021-11-23 Peng Chen , Jinsen Xiao

New Hardy type inequalities in sectorial area and as a limit in an exterior of a ball are proved. Sharpness of the inequalities is shown as well.

Analysis of PDEs · Mathematics 2021-03-17 Nikolai Kutev , Tsviatko Rangelov

We characterize certain weighted Hardy spaces on the unit disk and completely describe their dual spaces.

Complex Variables · Mathematics 2015-08-31 Nihat Gökhan Göğüş

We prove a Hardy inequality for ultraspherical expansions by using a proper ground state representation. From this result we deduce some uncertainty principles for this kind of expansions. Our result also implies a Hardy inequality on…

Classical Analysis and ODEs · Mathematics 2017-03-10 Alberto Arenas , Óscar Ciaurri , Edgar Labarga

In this paper we obtain logarithmic Hardy and Rellich inequalities on general Lie groups. In the case of graded groups, we also show their refinements using the homogeneous Sobolev norms. In fact, we derive a family of weighted logarithmic…

Analysis of PDEs · Mathematics 2021-07-13 Marianna Chatzakou , Aidyn Kassymov , Michael Ruzhansky

We give a new, simpler proof of the fractional Korn's inequality for subsets of $\mathbb{R}^d$. We also show a framework for obtaining Korn's inequality directly from the appropriate Hardy-type inequality.

Functional Analysis · Mathematics 2023-05-31 Artur Rutkowski

We prove non local Hardy inequalities on Carnot groups and Riemannian manifolds, relying on integral representations of fractional Sobolev norms.

Functional Analysis · Mathematics 2010-04-08 Emmanuel Russ , Yannick Sire

We prove non local Hardy inequalities on Carnot groups and Riemannian manifolds, relying on integral representations of fractional Sobolev norms.

Functional Analysis · Mathematics 2010-03-22 Emmanuel Russ , Yannick Sire

We prove local refined versions of Hardy's and Rellich's inequalities as well as of uncertainty principles for sums of squares of vector fields on bounded sets of smooth manifolds under certain assumptions on the vector fields. We also give…

Analysis of PDEs · Mathematics 2016-03-30 Michael Ruzhansky , Durvudkhan Suragan

In this paper, we prove the fractional Hardy inequality on polarisable metric measure spaces. The integral Hardy inequality for $1<p\leq q<\infty$ is playing a key role in the proof. Moreover, we also prove the fractional Hardy-Sobolev type…

Analysis of PDEs · Mathematics 2024-07-23 Aidyn Kassymov , Michael Ruzhansky , Gulnur Zaur

We study some Hardy-type inequalities involving a general norm in $R^n$ and an anisotropic distance function to the boundary. The case of the optimality of the constants is also addressed.

Analysis of PDEs · Mathematics 2015-12-18 Francesco Della Pietra , Giuseppina di Blasio , Nunzia Gavitone

We prove some Hardy-type inequalities via an approach that involves constructing auxiliary sequences.

Classical Analysis and ODEs · Mathematics 2015-06-26 Peng Gao

With the help of a radially invariant vector field, we derive inequalities of the Hardy kind, with no boundary terms, for $W^{1,p}$ functions on bounded star domains. Our results are not obtainable from the classical inequalities for…

Analysis of PDEs · Mathematics 2018-01-16 Ahmed A. Abdelhakim