自相似集上马尔科夫测度的加倍性质

该文讨论满足开集条件的自相似集上的马尔科夫测度,给出了马尔科夫测度具有加倍性质的一个充分必要条件.作为应用,刻画了几个具体的自相似集上具有加倍性质的马尔科夫测度.     

等价度量下的直径型填充测度

本文研究了在等价度量下,直径型填充测度之间的关系,证明了对任意紧度量空间(X,ρ),Pρ,g和Pcρ,g等价当且仅当纲函数g满足加倍条件.所得结论揭示了填充测度与加倍条件之间的关系.     

R上分段单调和分段加倍的加倍权

该文研究了R上几类权函数为加倍权的条件.首先给出了R上单调权函数为加倍权的充要条件;其次刻画了R上分段单调权函数为加倍权的条件;最后讨论了R上分段加倍权函数为加倍权的条件.     

半空间中一类调和函数的例外集

利用Whitney方体的相关性质, 给出了一类调和函数在半空间中无穷远点处的增长估计, 且刻画了其 例外集的几何性质. 本文推广了张艳慧和邓冠铁在半空间中的相关结果.     

紧空间上的正则向量值测度

J.Diestel和J.J.Uhl,Jr在他们的专著《Vector Measures》一书的第六章讨论了向量测度与C(Ω)上有界线性算子的关系。我们利用其中的一些结果得到紧空间上一类正则向量测度通过数值测度表示的定理。设Ω是紧Hausdorff空间,∑是Ω的所有Borel集构成的σ-代数,X是Banach空间,G:∑→X称为Ω上的正则X-值测度,若(i)当     

一类自相似集重分形分支的量纲

本文首先定义具有量纲函数的重分形测度,然后证明当Euclid空间中的两个重分形测度具有等价的量纲函数时,它们也等价.进一步,对于直线上满足强分离条件(SSC)的自相似集,在某些加倍条件下,本文给出判断其重分形分支的量纲函数的充要条件.     

Finsler度量测度空间上的容量

本文在Finsler度量测度空间上推广容量(capacity)理论,并研究对应的Sobolev空间.特别地,通过容量,本文给出Finsler度量测度空间上零边值Sobolev空间的完整刻画,并由此建立闭Finsler度量测度空间上的一个最优Hardy型不等式.     

向量值测度产生的集值测度及性质

由有界变差向量值测度的值域,通过取凸包和闭包,构造了L[0,1],L2[0,1]和C[0,1]空间上的有界变差紧凸集值测度,结果由欧氏空间推广到函数空间.     

距离空间上测度正则性的推广

本文给出了单调类与σ代数关系的充要条件,进一步得出距离空间的开集全体产生的最小单调类与产生的σ代数相等.利用这关系,证明了距离空间上的σ-有限测度也是正则测度.推广了距离空间上有限测度的正则性.     

测度空间上的gλ测度与条件gλ测度

本文在测度空间（Ｘ，μ）上引入了一类μ─密度函数ｆ所生成的ｇλ测度及条件ｇλ测度，并给出了与μ─密度函数ｆ相关的λ独立性的概念，得到了一些有关的结果     

Doubling measures on Whitney modification sets

A Whitney modification set in R is a set of the form E∪F(W), where E is a nonempty closed set in R, W is a Whitney decomposition of R?E, and F(W) consists of centers of intervals in W. We prove that a measure on a Whitney modification set is doubling if and only if it is the Whitney modification of a doubling measure on R.     

A counterexample concerning Whitney reversible properties

Two properties of continua are shown which are strong Whitney reversible while not sequential strong Whitney reversible. This answers an old question of S. B. Nadler, Jr.

     

Bases in the Spaces of C∞ -Functions on Cantor-Type Sets

We construct a topological basis in the space of Whitney functions given on the Cantor-type set.     

Whitney numbers of matroid extensions and co-extensions

Crapo found that single-element extensions of matroid are equivalent to modular cuts. This paper will study the single-element extension and co-extension of a matroid and establish the upper semi-continuity for the signless coefficients of Whitney polynomials and Whitney numbers on both extensions via its extension lattice, a lattice of all non-empty modular cuts.     

非齐型空间上分数型Marcinkiewicz积分算子的加权估计

令（X，d，μ）为满足所谓上倍双倍条件和几何双倍条件的度量测度空间.设M_β，ρ，q为（X，d，μ）上的分数型Marcinkiewicz积分算子.在本文中，作者证明了若β ∈[0，∞），ρ ∈（0，∞），q ∈（1，∞）且M_β，ρ，q在L²（μ）上有界，则M_β，ρ，q是从加权Lebesgue空间L^p（w）到加权弱Lebesgue空间L^p，∞（w）上有界和从加权Morrey空间L^p，κ，η（ω）到加权弱Morrey空间WL^p，κ，η（ω）上有界.     

DOUBLING MEASURES ON GENERALIZED CANTOR SETS

We study the doubling property of binomial measures on generalized ternary Cantor subsets of [0, 1]. We find some new phenomena. There are three different cases. In the first case, we obtain an equivalent condition for the measure to be doubling. In the other cases, we show that the condition is not necessary. Then facts and partial results are discussed.     

关于超空间上Whitney映射的一个问题

本文研究了超空间上的Ｗｎｉｔｎｅｙ映射,给出了它的一些性质和一个反例,从而解决了文献［１］中的一个问题．     

Whitney towers and gropes in 4-manifolds

Many open problems and important theorems in low-dimensional topology have been formulated as statements about certain 2-complexes called gropes. This paper describes a precise correspondence between embedded gropes in 4-manifolds and the failure of the Whitney move in terms of iterated `towers' of Whitney disks. The `flexibility' of these Whitney towers is used to demonstrate some geometric consequences for knot and link concordance connected to -solvability, -cobordism and grope concordance. The key observation is that the essential structure of gropes and Whitney towers can be described by embedded unitrivalent trees which can be controlled during surgeries and Whitney moves. It is shown that a Whitney move in a Whitney tower induces an IHX (Jacobi) relation on the embedded trees.