Fefferman-stein不等式和齐次群上Herz型Hardy空间的极大特征

本文延拓Fefferman-Stein加权极大不等式到齐次群上，作为其应用，建立了齐次群上伴随于Herz空间和Beurling代数的Hardy空间极大特征。同时，得到了具(α，r)型核的卷积算子在这些Hardy空间上的有界性。     

Interpolation and Embeddings of Weighted Tent Spaces

Given a metric measure space X, we consider a scale of function spaces \(T^{p,q}_s(X)\), called the weighted tent space scale. This is an extension of the tent space scale of Coifman, Meyer, and Stein. Under various geometric assumptions on X we identify some associated interpolation spaces, in particular certain real interpolation spaces. These are identified with a new scale of function spaces, which we call Z -spaces, that have recently appeared in the work of Barton and Mayboroda on elliptic boundary value problems with boundary data in Besov spaces. We also prove Hardy–Littlewood–Sobolev-type embeddings between weighted tent spaces.     

Embedding Derivatives and Integration Operators on Hardy Type Tent Spaces

Acta Mathematica Sinica, English Series - In this paper, we completely characterize the positive Borel measures μ on the unit ball $${mathbb{B}_n}$$ such that the differential type operator...     

一个积分不等式的证明及应用

利用概率技巧或H?lder不等式,可证∫Cxnf（x）dx ＞∫Cxf（x）dx ,其中 f （x）为连续型随机变量X的在其可能取值的区间C上的密度函数。     

Multidimensional Hilbert-type Inequality on the Weighted Orlicz Spaces

In this paper we derive multidimensional Hilbert-type inequality on the weighted Orlicz spaces with considerable attention given to homogeneous kernels of negative degree. As an application, we also deduce Hardy-Hilbert type inequality in one particular case. As a special case, we consider our general method in the case of the weighted Lebesgue spaces.     

Analogs of Markov's Inequality in Normed Spaces

Mathematical Notes -     

关于Banach空间中凸泛函的广义次梯度不等式

本文在前人^[1,2]的基础之上，以凸泛函的次梯度不等式为工具，将Jensen不等式推广到Banach空间中的凸泛函，导出了Banach空间中的Bochner积分型的广义Jensen不等式，给出其在Banach空间概率论中某些应用，从而推广了文献[3—6]的工作．     

畴数理论在纤维空间的应用

In this paper, we improve a result of James′ paper [1], and get the theorem; If P:E→B is a fibration, B is a normal space, and catB= n, then the composition of n filre-trivial maps is section homolopic.     

Application of the Trace Inequality to the Poisson Equation

The purpose of this paper is to show that solutions of the Poisson equation

An Extension of an Inequality Involving Symmetric Products with an Application to Permanents

Let A be an nk × nk positive semi-definite symmetric matrix partitioned into blocks A^ij each of which is an n × n matrix. In [2] Mine states a conjecture of Marcus that per(A) ≥ per(G) where G is the k × k matrix [per(A^ij)]. In this paper we prove a weaker inequality namely that per(A) ≥ (k!)^-1per(G).     

An Elementary Approach to Exponential Spaces

In 1970, Day and Kelly characterized exponential spaces by a condition (C). Eight years later, Hofmann and Lawson pointed out that this is equivalent to quasi-local compactness, i.e. every neighborhood V of a point contains a smaller one W such that any open cover of V admits a finite subcover of W. These characterizations work with topologies on topologies and may be felt to be not really elementary. This note instead offers an elementary approach which applies to quotient-reflective subcategories as well and includes a natural generalization of the compact-open topology on function spaces.     

Lower Semicontinuity of the Solution Map to a Parametric Generalized Variational Inequality in Reflexive Banach Spaces

This paper is concerned with the study of solution stability of a parametric generalized variational inequality in reflexive Banach spaces. Under the requirements that the operator of a unperturbed problem is of class (S)_?+? and operators under consideration are pseudo-monotone and demicontinuous, we show that the solution map of a parametric generalized variational inequality is lower semicontinuous. The obtained results are proved without conditions related to the degree theory and the metric projection.     

辅助函数在不等式证明中的应用

将不等式问题转化为函数问题,利用函数性质来研究、解决不等式问题.掌握不等式证明的一种函数思想方法,从而提高分析问题与解决问题的能力.     

An Operation Connected to a Young-Type Inequality

Given two φ-functions F and G we consider the largest φ-function H = F ⊕ G such that the Young-type inequality H(xy) ? F(x) + G(y) holds for all x, y > 0. We prove an equivalence theorem for F ⊕ G with the best constants and, for the special case when F and G are log-convex and satisfy a certain growth condition, a representation formula for F G. Moreover, further properties and examples are presented and the relations to similar results are discussed.     

An Extension of the Notion of Orthogonality to Banach Spaces

We extend the usual notion of orthogonality to Banach spaces. We show that the extension is quite rich in structure by establishing some of its main properties and consequences. Geometric characterizations and comparison results with other extensions are established. Also, we establish a characterization of compact operators on Banach spaces that admit orthonormal Schauder bases. Finally, we characterize orthogonality in the spaces l₂^p(C).     

Convergence Theorem for Variational Inequality in Hilbert Spaces with Applications

In this paper, we study variational inequality over the set of the common fixed points of a countable family of quasi-nonexpansive mappings. To tackle this problem, we propose an algorithm and use it to prove a strong convergence theorem under suitable conditions. As applications, we study variational inequality over the solution set of different nonlinear or linear problems, like minimization problems, split feasibility problems, convexly pseudoinverse problems, convex linear inverse problems, etc.     

关于内积空间中逆Cauchy-Schwarz不等式的一些结果

Some new reverses of the Cauchy-Schwarz inequality in inner product spaces are presented in this paper. As an application of the main result, a formula for error estimate concerning Cauchy-Schwarz‘s inequality is provided. The results obtained in the paper complement and improve some recent work about this topic.     

Banach空间中混合变分不等式解的存在性

By using the property of generalized f-projection operator and FKKM theorem, the existence theorem of solutions for the mixed variational inequality is proved under weaker assumption in reflexive and smooth Banach space. The results improve and extend the corresponding results shown recentlv.