广义Greiner算子的几类Hardy型不等式

对构成广义Greiner算子的向量场$X_j = \frac{\partial }{\partial x_j} + 2ky_j \vert z\vert ^{2k - 2}\frac{\partial }{\partialt}$, $Y_j = \frac{\partial }{\partial y_j } - 2kx_j \vert z\vert^{2k - 2}\frac{\partial }{\partial t}$, j = 1,... ,n, x,y∈ Rⁿ, $z = x + \sqrt { - 1} \,y$, t ∈ R, k ≥1, 得到了拟球域内和拟球域外的Hardy型不等式;建立了广义Picone型恒等式,并由此导出比文献[3]更一般的全空间上的Hardy型不等式;并在$p = 2$时建立了具最佳常数的Hardy型不等式.     

与广义Baouendi-Grushin向量场相联系的Hardy不等式及其应用

本文建立一类与广义Baouendi—Grushin向量场联系的Hardy不等式．采用的技巧是延伸欧氏空间上的散度定理推出的基本积分不等式和选定适当的向量场．Hardy不等式相应的最佳常数也得到证明．本文结果包括了已有广义Baouendi-Grushin向量场的Hardy不等式．作为应用，讨论了由Baouendi-GrusMn向量场构成一退化次椭圆算子的一些性质和刻画了这类向量场构成的非线性算子的一个正解．     

Some new Stein and Hardy type inequalities

We prove a generalization of the pointwise Stein inequality, considering two truncated versions. More generally than in the Stein inequality, we assume that the kernel is dominated by a radial function almost decreasing after the division by a power function with nonnegative exponent in the case of the truncation to the ball of the radius and almost increasing after the multiplication by a power function in the case of truncation to the exterior of this ball. We give some applications to a series of inequalities of Hardy type in norms of various function spaces, in particular, in the norm of variable exponent Lebesgue spaces L^{p( ·)}( \mathbbRⁿ ) {L^{p\left( \cdot \right)}}\left( {{{\mathbb{R}}^n}} \right) with weights. Bibliography: 40 titles.     

Some Hardy Type Inequalities in R~n

Some Hardy type inequalities on the ball and its complementary set in the Euclidean space are established by using the Picone type identity and constructing suitable auxiliary functions.     

Local Poincaré inequalities in non-negative curvature and finite dimension

In this paper, we derive a new set of Poincaré inequalities on the sphere, with respect to some Markov kernels parameterized by a point in the ball. When this point goes to the boundary, those Poincaré inequalities are shown to give the curvature-dimension inequality of the sphere, and when it is at the center they reduce to the usual Poincaré inequality. We then extend them to Riemannian manifolds, giving a sequence of inequalities which are equivalent to the curvature-dimension inequality, and interpolate between this inequality and the Poincaré inequality for the invariant measure. This inequality is optimal in the case of the spheres.     

On slice hyperholomorphic fractional Hardy spaces

In this paper we introduce and study the fractional Hardy spaces of the half space and of the unit ball in the quaternionic setting. In particular, we discuss their properties of invariance and of factorization in terms of functions in the Hardy space of the half space in the first case, and in terms of a suitable reproducing kernel Hilbert space in the case of the unit ball.     

L 1 Hardy Inequalities with Weights

We prove sharp homogeneous improvements to L ¹ weighted Hardy inequalities involving distance from the boundary. In the case of a smooth domain, we obtain lower and upper estimates for the best constant of the remainder term. These estimates are sharp in the sense that they coincide when the domain is a ball or an infinite strip. In the case of a ball, we also obtain further improvements.     

Improved Poincaré inequalities

Although the Hardy inequality corresponding to one quadratic singularity, with optimal constant, does not admit any extremal function, it is well known that such a potential can be improved, in the sense that a positive term can be added to the quadratic singularity without violating the inequality, and even a whole asymptotic expansion can be built, with optimal constants for each term. This phenomenon has not been much studied for other inequalities. Our purpose is to prove that it also holds for the gaussian Poincaré inequality. The method is based on a recursion formula, which allows to identify the optimal constants in the asymptotic expansion, order by order. We also apply the same strategy to a family of Hardy–Poincaré inequalities which interpolate between Hardy and gaussian Poincaré inequalities.     

Riemann-Hilbert problems for poly-Hardy space on the unit ball

In this paper, we focus on a Riemann–Hilbert boundary value problem (BVP) with a constant coefficients for the poly-Hardy space on the real unit ball in higher dimensions. We first discuss the boundary behaviour of functions in the poly-Hardy class. Then we construct the Schwarz kernel and the higher order Schwarz operator to study Riemann–Hilbert BVPs over the unit ball for the poly-Hardy class. Finally, we obtain explicit integral expressions for their solutions. As a special case, monogenic signals as elements in the Hardy space over the unit sphere will be reconstructed in the case of boundary data given in terms of functions having values in a Clifford subalgebra. Such monogenic signals represent the generalization of analytic signals as elements of the Hardy space over the unit circle of the complex plane.     

Hardy–Littlewoodʼs inequalities in the case of a capacity

Hardy–Littlewood?s inequalities, well known in the case of a probability measure, are extended to the case of a monotone (but not necessarily additive) set function, called a capacity. The upper inequality is established in the case of a capacity assumed to be continuous and submodular, the lower — under assumptions of continuity and supermodularity.     

HEISENBERG-GREINER p-退化椭圆算子的一类HARDY不等式及其应用

本文研究了p-退化椭圆Heisenberg-Greiner算子的一类Hardy不等式的证明问题.利用正则化及逼近的方法,获得了该算子的一类强Hardy不等式的结果,推广了已有文献中p的取值范围,并进一步弥补了去除原点的缺陷.作为应用,讨论了与该算子相关的一类非线性算子的正定性与下无界性,并给出了它的一个正解.     

Further bounds for hardy type differences

In this paper we define a functional as a difference between the right-hand side and left-hand side of the refined Boas type inequality using the notation of superquadratic and subquadratic functions and study its properties, such as exponential and logarithmic convexity. We also, state and prove improvements and reverses of new weighted Boas type inequalities. As a special case of our result we obtain improvements and reverses of the Hardy inequality and its dual inequality. We introduce new Cauchy type mean and prove monotonicity property of this mean.     

Hardy–Littlewood–Sobolev and Stein–Weiss inequalities on homogeneous Lie groups

In this note, we prove the Stein–Weiss inequality on general homogeneous Lie groups. The obtained results extend previously known inequalities. Special properties of homogeneous norms play a key role in our proofs. Also, we give a simple proof of the Hardy–Littlewood–Sobolev inequality on general homogeneous Lie groups.     

A functional framework for the Keller–Segel system: Logarithmic Hardy–Littlewood–Sobolev and related spectral gap inequalities

This Note is devoted to several inequalities deduced from a special form of the logarithmic Hardy–Littlewood–Sobolev, which is well adapted to the characterization of stationary solutions of a Keller–Segel system written in self-similar variables, in case of a subcritical mass. For the corresponding evolution problem, such functional inequalities play an important role for identifying the rate of convergence of the solutions towards the stationary solution with same mass.     

A general rearrangement inequality for multiple integrals

In this paper we prove a rearrangement inequality that generalizes inequalities given in the book by Hardy, Littlewood and Pólya¹ and by Luttinger and Friedberg.² The inequality for an integral of a product of functions of one variable is further extended to the case of functions of several variables.     

Conformal metrics on the ball with zero scalar curvature and prescribed mean curvature on the boundary

This paper considers the prescribed zero scalar curvature and mean curvature problem on the n-dimensional Euclidean ball for n?3. We consider the limits of solutions of the regularization obtained by decreasing the critical exponent. We characterize those subcritical solutions which blow-up at the least possible energy level, determining the points at which they can concentrate, and their Morse indices. We show that when n=3 this is the only blow-up which can occur for solutions. We use this in combination with the Morse inequalities for the subcritical problem to obtain a general existence theorem for the prescribed zero scalar curvature and mean curvature on the three-dimensional Euclidean ball. In the higher-dimensional case n?4, we give conditions on the function h to guarantee there is only one simple blow-up point.     

Heisenberg型群上的几类Hardy型不等式

文章得到了Heisenberg型群上的几类Hardy型不等式,并确定出了次Laplace算子的Hardy型不等式中的最佳常数．     

Weighted composition operators from the weighted Bergman space to the weighted Hardy space on the unit ball

We investigate the weighted composition operator from the weighted Bergman space into the weighted Hardy space on the unit ball. As a consequence of the investigation, we also give a characterization for the boundedness and compactness of the operator whose the target space is the Hardy space.     

单位球上不同Hardy空间之间的复合算子

研究了C~N中单位球B上,当q相似文献   

Sobolev-Lorentz范数约束下的次临界型Adams不等式

本文在Sobolev-Lorentz空间W2L2,q(R4)的范数约束下得到了一个最佳的二阶次临界型Adams不等式.进一步,当次临界指标逼近最佳常数时,得到了Adams泛函的上、下界的估计.本文主要采用了Lam和Lu[A new approach to sharp Moser-Trudinger and Adams ...