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Related papers: Unified weighted Hardy-type inequalities

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We present a symmetry-based framework for equilibrium statistical mechanics that formulates a single Lie group combining conventional spacetime symmetries with a recently identified phase-space gauge-shifting invariance [Muller et al.,…

Statistical Mechanics · Physics 2026-04-02 Hai Pham-Van

We continue our investigation of Hardy-type inequalities involving combinations of cylindrical and spherical weights. Compared to [Cora-Musina-Nazarov, Ann. Sc. Norm. Sup., 2024], where the quasi-spherical case was considered, we handle the…

Analysis of PDEs · Mathematics 2024-11-14 Roberta Musina , Alexander I. Nazarov

We show that the sharp constant in the classical $n$-dimensional Hardy-Leray inequality can be improved for axisymmetric divergence-free fields, and find its optimal value. The same result is obtained for $n=2$ without the axisymmetry…

Classical Analysis and ODEs · Mathematics 2007-05-23 O. Costin , V. Maz'ya

We establish an equivariant generalization of the Novikov inequalities which allow to estimate the topology of the set of critical points of a closed basic invariant 1-form by means of twisted equivariant cohomology of the manifold. We test…

dg-ga · Mathematics 2008-02-03 Maxim Braverman , Michael Farber

In this paper we obtain some sharp Hardy inequalities with weight functions that may admit singularities on the unit sphere. In order to prove the main results of the paper we use some recent sharp inequalities for the lowest eigenvalue of…

Analysis of PDEs · Mathematics 2014-08-26 Thomas Hoffmann-Ostenhof , Ari Laptev

We present a generic functional inequality on Riemannian manifolds, both in additive and multiplicative forms, that produces well known and genuinely new Hardy-type inequalities. For the additive version, we introduce Riccati pairs that…

Analysis of PDEs · Mathematics 2024-02-16 Sándor Kajántó , Alexandru Kristály , Ioan Radu Peter , Wei Zhao

By a systematic development of fundamental concepts of conformable calculus we establish conformable divergence theorem and Green's identities which we combine with some new anisotropic Picone type identities to derive a generalized…

Analysis of PDEs · Mathematics 2024-12-03 Abimbola Abolarinwa , Yisa O Anthony

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

In this note we give several characterisations of weights for two-weight Hardy inequalities to hold on general metric measure spaces possessing polar decompositions. Since there may be no differentiable structure on such spaces, the…

Functional Analysis · Mathematics 2019-12-24 Michael Ruzhansky , Daulti Verma

The aim of this paper is to establish weighted Hardy type inequality in a broad family of means. In other words, for a fixed vector of weights $(\lambda_n)_{n=1}^\infty$ and a weighted mean $\mathscr{M}$, we search for the smallest number…

Classical Analysis and ODEs · Mathematics 2020-12-07 Zsolt Páles , Paweł Pasteczka

In this paper we establish the subelliptic Picone type identities. As consequences, we obtain Hardy and Rellich type inequalities for anisotropic p-sub- Laplacians which are operators of the form $$ \mathcal{L}_p f :=…

Analysis of PDEs · Mathematics 2020-05-07 Michael Ruzhansky , Bolys Sabitbek , Durvudkhan Suragan

We develop a unified framework for a broad class of nonlocal elliptic problems, encompassing a wide spectrum of nonlocal terms, including the classical Kirchhoff and Carrier-type equations as particular cases, and nonlinearities having…

Analysis of PDEs · Mathematics 2026-03-25 L. Gasinski , H. Ramos Quoirin , J. Santos Junior , K. Silva

In this paper, Heisenberg-Pauli-Weyl-type uncertainty inequalities are obtained for a pair of positive-self adjoint operators on a Hilbert space, whose spectral projectors satisfy a ``balance condition'' involving certain operator norms.…

Functional Analysis · Mathematics 2013-03-08 Alessio Martini

We establish Hardy inequalities involving a weight function on complete, not necessarily reversible Finsler manifolds. We prove that the superharmonicity of the weight function provides a sufficient condition to obtain Hardy inequalities.…

Differential Geometry · Mathematics 2020-10-14 Ágnes Mester , Ioan Radu Peter , Csaba Varga

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 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…

Analysis of PDEs · Mathematics 2020-12-17 Xiaojing Liu , Toshio Horiuchi , Hiroshi Ando

Recently, Yanyan Li and Xukai Yan showed the following interesting Hardy inequalities with anisotropic weights: Let $n\geq 2$, $p \geq 1$, $p\alpha > 1-n$, $p(\alpha + \beta)> -n$, then there exists $C > 0$ such that…

Analysis of PDEs · Mathematics 2025-03-11 Xia Huang , Dong Ye

In this paper we prove sharp multipolar Hardy-type inequalities in the Riemannian $L^p-$setting for $p\geq 2$ using the method of super-solutions and fundamental results from comparison theory on manifolds, thus generalizing previous…

Analysis of PDEs · Mathematics 2025-03-07 Cristian Ciulică , Teodor Rugină

We establish a new improvement of the classical $L^p$-Hardy inequality on the multidimensional Euclidean space in the supercritical case. Recently, in [14], there has been a new kind of development of the one dimensional Hardy inequality.…

Functional Analysis · Mathematics 2024-01-12 Prasun Roychowdhury , Michael Ruzhansky , Durvudkhan Suragan

We define Euler-Hilbert-Sobolev spaces and obtain embedding results on homogeneous groups using Euler operators, which are homogeneous differential operators of order zero. Sharp remainder terms of $L^{p}$ and weighted Sobolev type and…

Functional Analysis · Mathematics 2018-01-24 Michael Ruzhansky , Durvudkhan Suragan , Nurgissa Yessirkegenov