共轭A-调和张量的双权Hardy-Littlewood不等式

本文证明了共轭A-调和张量的局部双权积分不等式,此结果类似于共轭调和函数的古典Hardy-Littlewood不等式.作为局部结果的应用,还证明了John域上的共轭A-调和张量的全局双权积分不等式.     

共轭A-调和张量的双权Hardy-Littlewood不等式

本文证明了共轭A-调和张量的局部双权积分不等式,此结果类似于共轭调和函数的古典Hardy-Littlewood不等式.作为局部结果的应用,还证明了John域上的共轭A-调和张量的全局双权积分不等式.     

弱A-调和张量的奇点可去性

该文研究微分形式的A-调和方程d~*A(x,du)=0,通过Hodge分解建立弱A-调和张量的Caccioppoli不等式,获得了弱A-调和张量的奇点可去性.     

图上曲率维数不等式的若干等价性质

本文研究局部有限图上的曲率维数不等式CD(n,K)的若干等价性质,包括梯度估计、Poincaré不等式和逆Poincaré不等式.还得到了局部有限图上的修正曲率维数不等式CDE′(∞,K)的其中一个等价性质,即梯度估计.     

加权Sobolev空间中的Poincaré不等式

在加权Sobolov空间中讨论了加权的Poincaré不等式,利用嵌入映射给出了加权Poincaré不等式成立的充分和必要条件．     

有界域上局部与全局的Radon测度的积分不等式

选择Laplace-Beltrami算子Δ和Green算子G的复合算子Δ◇G为研究对象,首先证明了有界域的局部圆域上作用于齐次A-调和方程解的复合算子Δ◇G的带Radon测度的积分不等式,然后在此基础上得到有界域上全局的Radon积分不等式.     

具有非标准增长条件的微分形式的Caccioppoli不等式及其高阶可积性（英文）

本文主要研究了微分形式中的相关不等式.利用A-调和方程的性质及与该方程相关的弱逆Holder不等式和一类满足非标准增长条件的Young函数的性质,获得了一类特殊的微分形式(即非齐次A-调和张量)在该类Young函数作用下的Caccoppoli不等式及其高阶可积性.该结论将微分形式中Caccoppoli不等式由Lp空间推广到了由该类Young函数构成的Orlicz空间,同时验证了该Caccoppoli不等式可以用于微分形式的定量估计和定性分析.     

Cauchy测度的两类加权泛函不等式

研究了一维Cauchy分布的加权Poincaré不等式和加权log-Sobolev不等式.我们给出并证明了所给权函数的最优性,同时对不等式中的常数进行了阶的估计.     

共轭A-调和张量新的双权积分不等式

共轭A-调和张量的一些局部Aλr3(λ1,λ2,Ω)-加权积分不等式得到了证明,它们可看作是共轭调和函数和p-调和函数相应结果的推广.这些结果可用来研究共轭调和函数的可积性并估计它们的积分.同时也给出上述结果在拟正则映射中的应用.     

目标流形为Heisenberg群能量极小映射的逆Poincardé不等式

研究目标流形为Heisenberg群能量极小映射的性质,得到关于能量极小映射的逆Poincaré不等式.     

关于一般矩阵函数变差的不等式

该文首先展示了一般矩阵函数dχ(A)=∑[DD(X]σ∈H[DD)]χ(σ)∏[DD(]m[]i=1[DD)]aiσ(i)可作为一个酉空间张量的适当对称类的内积.然后，借助Schwarz不等式和范数证明了关于一般矩阵函数变差的三个主要不等式,而其中一个不等式是已知不等式的推广.     

The structure vector field and structure Jacobi operator of real hypersurfaces in nonflat complex space forms

In this paper we determine the real hypersurfaces for which the structure Jacobi operator commutes over both the Ricci tensors and structure tensors (for a definition of the operator see Sect. 1). We prove that such hypersurfaces are homogneous real hypersurfaces of type (A) and are a special class of Hopf hypersurfaces.     

Improved Chen–Ricci inequality for curvature-like tensors and its applications

We present Chen–Ricci inequality and improved Chen–Ricci inequality for curvature like tensors. Applying our improved Chen–Ricci inequality we study Lagrangian and Kaehlerian slant submanifolds of complex space forms, and C-totally real submanifolds of Sasakian space forms.     

Weighted Hardy-Littlewood inequality for -harmonic tensors

In this paper we prove a local weighted integral inequality for conjugate -harmonic tensors similar to the Hardy and Littlewood integral inequality for conjugate harmonic functions. Then by using the local weighted integral inequality, we prove a global weighted integral inequality for conjugate -harmonic tensors in John domains.

     

Tensor Bernstein concentration inequalities with an application to sample estimators for high-order moments

This paper develops the Bernstein tensor concentration inequality for random tensors of general order,based on the use of Einstein products for tensors.This establishes a strong link between these and matrices,which in turn allows exploitation of existing results for the latter.An interesting application to sample estimators of high-order moments is presented as an illustration.     

Weighted integral inequalities for conjugate A-harmonic tensors

We first prove a local weighted integral inequality for conjugate A-harmonic tensors. Then, as an application of our local result, we prove a global weighted integral inequality for conjugate A-harmonic tensors in L^s(μ)-averaging domains, which can be considered as a generalization of the classical result. Finally, we give applications of the above results to quasiregular mappings.     

On the Bohr inequality of operators

This paper is focused on the operator inequalities of the Bohr type. We will give a new and transparent proof for the operator Bohr inequality through an absolute value operator identity, show some related operator inequalities by means of 2×2 (block) operator matrices, and finally we will present a generalization of the operator Bohr inequality for multiple operators.     

Factorization strategies for third-order tensors

Operations with tensors, or multiway arrays, have become increasingly prevalent in recent years. Traditionally, tensors are represented or decomposed as a sum of rank-1 outer products using either the CANDECOMP/PARAFAC (CP) or the Tucker models, or some variation thereof. Such decompositions are motivated by specific applications where the goal is to find an approximate such representation for a given multiway array. The specifics of the approximate representation (such as how many terms to use in the sum, orthogonality constraints, etc.) depend on the application.In this paper, we explore an alternate representation of tensors which shows promise with respect to the tensor approximation problem. Reminiscent of matrix factorizations, we present a new factorization of a tensor as a product of tensors. To derive the new factorization, we define a closed multiplication operation between tensors. A major motivation for considering this new type of tensor multiplication is to devise new types of factorizations for tensors which can then be used in applications.Specifically, this new multiplication allows us to introduce concepts such as tensor transpose, inverse, and identity, which lead to the notion of an orthogonal tensor. The multiplication also gives rise to a linear operator, and the null space of the resulting operator is identified. We extend the concept of outer products of vectors to outer products of matrices. All derivations are presented for third-order tensors. However, they can be easily extended to the order-p(p>3) case. We conclude with an application in image deblurring.     

New sharp inequalities for operator means

New sharp multiplicative reverses of the operator means inequalities are presented, with a simple discussion of squaring an operator inequality. As a direct consequence, we extend the operator Pólya-Szegö inequality to arbitrary operator means. Furthermore, we obtain some new lower and upper bounds for the Tsallis relative operator entropy, operator monotone functions and positive linear maps.