On weighted remainder form of Hardy-type inequalities
Peng Gao
我们使用不同的方法来研究Levin和Stečkin关于一个类似于Hardy不等式的不等式的结果的推广。我们的结果自然地导致了Hardy型不等式的加权余式的研究。
We use different approaches to study a generalization of a result of Levin and Stečkin concerning an inequality analogous to Hardy's inequality. Our results lead naturally to the study of weighted remainder form of Hardy-type inequalities.
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本文研究Baouendi-Grushin向量场：$\nabla_γ=(\nabla_x, |x|^{2γ}\nabla_y)$的Hardy型和Rellich型不等式，其中$γ>0$，$\nabla_x$和$\nabla_y$分别是变量$x\in \mathbb{R}^m$和$y\in\mathbb{R}^k$的常用梯度算子.本文第一部分证明了几个带余项的加权Hardy型不等式。第二部分证明了全空间上的两个加权Rellich型不等式。我们发现这些不等式的尖锐常数。我们也得到了他们的改进版本的有界域。
Some trace Hardy type inequalities and trace Hardy-Sobolev-Maz'ya type inequalities
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Hardy and Rellich inequalities, identities, and sharp remainders on homogeneous groups
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利用分数阶Sobolev范数的整表示，证明了Carnot群和黎曼流形上的非局部Hardy不等式.
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Generalized affine Hardy-Littlewood-Sobolev inequalities
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Hardy-Poincaré, Rellich and Uncertainty principle inequalities on Riemannian manifolds
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On the necessity of the assumptions used to prove Hardy-Littlewood and Riesz Rearrangement Inequalities 1
证明了超模性是广义Hardy-Littlewood和Riesz重排不等式成立的必要条件.我们还证明了Riesz{型积分的核的单调性的必要性。
Factorizations and Hardy-Rellich inequalities on stratified groups
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Abstract framework for John Nirenberg inequalities and applications to Hardy spaces
在本文中，我们发展了一个抽象的框架，约翰-尼伦伯格不等式与BMO型空间。这项工作可以被看作是[5]的续集，在[5]中，作者介绍了原子和分子Hardy空间的一个非常一般的框架。此外，我们表明，我们的假设允许我们恢复一些已知的John-Nirenberg不等式。我们也给出了原子Hardy空间的应用。
In this paper we focus our attention on an embedding result for a weighted Sobolev space that involves as weight the distance function from the boundary taken with respect to a general smooth gauge function $F$. Starting from this type of inequalities we prove some refined Hardy-type inequalities.
Unified weighted Hardy-type inequalities
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Hardy-Sobolev-Rellich, Hardy-Littlewood-Sobolev and Caffarelli-Kohn-Nirenberg inequalities on general Lie groups
该研究在一般连通李群的次椭圆微分算子框架下，建立了多类几何不等式及其临界形式，覆盖不同拓扑与模性情形，并推导了对应的不确定型原理。
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Iterated Hardy-type inequalities involving suprema
本文给出了上算子的限制不等式的完全解。在加权Lebesgue空间中刻画了上实算子与Hardy算子和Copson算子的复合的有界性。
Refined general weighted $L^{p}$-Hardy and Caffarelli-Kohn-Nirenberg type inequalities and identities related to the Baouendi-Grushin operator
本文研究与Baouendi-Grushin算子相关的不等式问题，给出非负权对的充分条件以得到一般加权$L^p$-Hardy型恒等式，改进已有结果，并推导带余项的Caffarelli-Kohn-Nirenberg型不等式及Heisenberg-Pauli-Weyl型不等式。
Hardy inequalities with boundary singularities
本文证明了二次奇异位势局部化在光滑区域边界上的Hardy-Poincaré不等式。然后，我们考虑了顶点在奇点上的锥域，给出了Hardy不等式中相应的最优常数的上界和下界。特别地，我们证明了最佳常数的渐近行为时，槽锥趋于零。
The sharp higher order Hardy--Rellich type inequalities on the homogeneous groups
证明了齐次群上高阶导数积分的几个有趣的等式。作为推论，我们得到了齐次群上高阶导数的Hardy-Rellich型不等式，包括次临界和临界不等式.我们还证明了齐次群上的几个测不准原理。我们的结果在欧几里得空间$\mathbb R^n$中也是新的，并给出了$\mathbb R^n$中几个经典Hardy-Rellich型不等式的简单证明.
The notion of multipolynomials was recently introduced and explored by T. Velanga in [10] as an attempt to encompass the theories of polynomials and multi- linear operators. In the present paper we push this subject further, by proving Hardy- Littlewood inequalities for multipolynomials and, en passant, a variant of the Kahane- Salem-Zygmund inequality in this framework.
Sharp Weight Hardy-Sobolev inequalities for Grand Lebesgue Spaces
本文给出了在整个多维欧几里得空间上作用于两个权大Lebesgue空间（GLS）之间的两个Hardy-Sobolev型算子范数的精确值.
A note on stability of Hardy inequalities
在本说明中，我们制定了最近的稳定性结果的哈迪不等式的语言Folland和Stein的齐次群。从而得到了齐次群上Rellich型不等式的余项估计.与欧几里德结果的主要区别在于，所得到的稳定性估计对任何齐次拟范数都成立。
Power-weighted Hardy type integral inequalities with additional terms on finite intervals
本文研究有限区间上的积分Hardy型不等式，证明新的L2和Lp不等式，常数依赖于Bessel函数对应Lamb型方程的首根，并给出极值函数和多维推广。
We provide a precise statement and self contained proof of a Sobolev inequality (cf. [A, page 236 and page 237]) stated in the original paper. Higher order and fractional inequalities are treated as well.
Hardy-Hilbert type inequalities on homogeneous groups-An introduction and generalization to the kernel case
本文介绍齐次群上Hardy-Hilbert型不等式的发展，将经典情形的若干该类不等式统一为一般核情形，并把结果推广至齐次群情形。
This paper is devoted to Hardy type inequalities with remainders for compactly supported smooth functions on open sets in the Euclidean space. We establish new inequalities with weight functions depending on the distance function to the boundary of the domain. One-dimensional $L_1$ and $L_p$ inequalities and their multidimensional analogues are proved. We consider spatial inequalities in open convex domains with the finite inner radius. Constants in these inequalities depend on the roots of parametric Lamb equation for the Bessel function and turn out to be sharp in some particular cases.
A note on Hardy-type inequalities in variable exponent Lebesgue spaces
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Hardy-Littlewood inequalities for norms of positive operators on sequence spaces
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Hardy and Hardy PDO type inequalities in domains. Part I
前面的“索伯列夫空间中的多项式容量、Poincare型不等式和谱综合“是本文的前提。推荐平行阅读。
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这是哈代不等式发展的一条主线.
Sharp Hardy type inequalities on the Carnot Group
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It is known that classical Hardy and Sobolev inequalities hold when the exponent $p$ and the dimension $N$ satisfy $p < N < \infty$. In this note, we consider two limits of Hardy and Sobolev inequalities as $p \nearrow N$ and $N \nearrow \infty$ in some sense.
Improved Hardy and Rellich inequalities on Riemannian manifolds
本文建立了黎曼流形$M$上改进的Hardy和Rellich型不等式.此外，还得到了双曲空间$\mathbb{H}^n$上改进的Hardy不等式的精确常数和Rellich不等式的显式常数.
Best constants for Hardy inequalities in Triebel--Lizorkin spaces
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Hardy, Rellich and Uncertainty principle inequalities on Carnot Groups
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We study Hardy-type inequalities on infinite homogeneous trees. More precisely, we derive optimal Hardy weights for the combinatorial Laplacian in this setting and we obtain, as a consequence, optimal improvements for the Poincaré inequality.
The purpose of this text is twofold. We present a review of the existing stability results for Sobolev, Hardy-Littlewood-Sobolev (HLS) and related inequalities. We also contribute to the topic with some observations on constructive stability estimates for (HLS).
The Dirac-Hardy and Dirac-Sobolev inequalities in $L^1$
建立了$L^1$中的Dirac-Sobolev和Dirac-Hardy不等式，其中用弱$L^p$空间代替了经典Sobolev和Hardy不等式中的$L^p$空间.对Loss和Yau构造的适当Pauli算子的零模给出了与经典不等式类似的反例。
Extensions of the Inequalities of Hardy and Hilbert
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Weighted $L^p$-Hardy and $L^p$-Rellich inequalities with boundary terms on stratified Lie groups
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We establish improved versions of the Hardy and Caffarelli-Kohn-Nirenberg inequalities by replacing the standard Dirichlet energy with some nonlocal nonconvex functionals which have been involved in estimates for the topological degree of continuous maps from a sphere into itself and characterizations of Sobolev spaces.
We prove sharp inequalities of Hardy type for functions in the Sobolev space $W^{1,p}$ on the unit sphere $\mathbb{S}^{n-1}$ in $\mathbb{R}^{n}$. We achieve this in both the subcritical and critical cases. The method we use to show optimality takes into account all the constants involved in our inequalities.
Weight Hardy-Littlewood Inequalities for Different Powers
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Sharp Hardy-Littlewood-Sobolev Inequalities on Octonionic Heisenberg Group
本文是继我们的工作[CLZ 13]之后的第二篇，研究Heisenberg型群上的Hardy-Littlewood-Sobolev不等式.第一个重要的突破是弗兰克和利布在[FL 12]中取得的。本文对八元数海森堡群也得到了类似的结果。
Affine Hardy--Littlewood--Sobolev inequalities
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Sharp fractional Hardy inequalities in half-spaces
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