Two properties of sequence of vector measures on effect algebras

Let (L,⊕,0,1) be an effect algebra and let X be a Banach space. A function μ : L → X is called a vector measure if μ(a ⊕ b) = μ(a) + μ(b) whenever a⊥b in L. The function μ is said to be s-bounded if lim n→∞μ(a n ) = 0 in X for any orthogonal sequence (a n ) n∈N in L. In this paper, we introduce two properties of sequence of s-bounded vector measures and give some results on these properties.     

Banach空间中有限族渐进伪压缩映象的迭代程序

Let E be a real Banach space and K be a nonempty closed convex and bounded subset of E. Let Ti ： K→ K, i=1, 2,... ,N, be N uniformly L-Lipschitzian, uniformly asymptotically regular with sequences {ε^（i）n} and asymptotically pseudocontractive mappings with sequences {κ^（i）n}, where {κ^（i）n} and {ε^（i）n}, i = 1, 2,... ,N, satisfy certain mild conditions. Let a sequence {xn} be generated from x1 ∈ K by zn：= （1-μn）xn＋μnT^nnxn, xn＋1 ：= λnθnx1＋ [1 - λn（1 ＋ θn）]xn ＋ λnT^nnzn for all integer n ≥ 1, where Tn = Tn（mod N）, and {λn}, {θn} and {μn} are three real sequences in [0, 1] satisfying appropriate conditions. Then ｜｜xn- Tixn｜｜→ 0 as n→∞ for each l ∈ {1, 2,..., N}. The results presented in this paper generalize and improve the corresponding results of Chidume and Zegeye, Reinermann, Rhoades and Schu.     

带非双倍测度的BMO空间的一个注记

Let μ be a positive Radon measure which only satisfies an appropriate growth condition, and RBMO(μ) be the BMO space associated with μ which was introduced by Tolsa. In this paper, it is proved that the definition of RBMO(p) can be weakened sufficiently.Key words: RBMO(μ); non doubling measure; doubling cube     

BOUNDEDNESS OF STEIN＇S SQUARE FUNCTIONS ASSOCIATED TO OPERATORS ON HARDY SPACES

Let(X, d, μ) be a metric measure space endowed with a metric d and a nonnegative Borel doubling measure μ. Let L be a second order non-negative self-adjoint operator on L2(X). Assume that the semigroup e-tLgenerated by L satisfies the Davies-Gaffney estimates. Also, assume that L satisfies Plancherel type estimate. Under these conditions,we show that Stein's square function Gδ(L) arising from Bochner-Riesz means associated to L is bounded from the Hardy spaces Hp L(X) to Lp(X) for all 0 p ≤ 1.     

A Note on the BMO Space with Non-doubling Measure

Let μi be a positive Radon measure which only satisfies an appropriate growth condition, and RBMO(μ) be the BMO space associated with μ which was introduced by Tolsa. In this paper, it is proved that the definition of RBMO(ρ) can be weakened sufficiently.     

Generalization for Laplacian energy

Let G be a simple graph with n vertices and m edges. Let λ1, λ2,…, λn, be the adjacency spectrum of G, and let μ1, μ2,…, μn be the Laplacian spectrum of G. The energy of G is E（G） = n∑i=1｜λi｜, while the Laplacian energy of G is defined as LE（G） = n∑i=1｜μi-2m/n｜ Let γ1, γ2, ~ …, γn be the eigenvalues of Hermite matrix A. The energy of Hermite matrix as HE（A） = n∑i=1｜γi-tr（A）/n｜ is defined and investigated in this paper. It is a natural generalization of E（G） and LE（G）. Thus all properties about energy in unity can be handled by HE（A）.     

(0,1)-矩阵类u(R,S)的基数函数f(R,S)及其非零集

Let R and S be two vectors with m and n nonnegative integers as conponents respectively. Let u(R, S) be the class consisting of all m×n (0,1) - matrices with row sum vector R and column sum vector S. Suppose that A is the maximal mrixat with row sum vector R. Let S he the column sum vector of A. (of. H. J. Ryser, Combinatorial Mathematics, Carcus Math. Monograph 14 (1963)). Let L(S)={S=(s₁,…,s_m),S-1≥s₂≥…≥s_n}, and let F(R, S) be the cardinal function of u(R,S), i. e.. f(R, S) = |u(R, S) |. Then L(S) is the nonzero-point set of f(R,S). In this paper our principal result is the following.     

Weighted estimates for iterated commutators of multilinear Calderón-Zygmund operators on non-homogeneous metric measure spaces

Let(X, d, μ) be a non-homogeneous metric measure space satisfying the so-called upper doubling and geometrically doubling conditions, which includes the space of homogeneous type and the Euclidean space with the non-doubling measure as special cases. Let T be a multilinear Calderón-Zygmund operator and ■:=(b1,..., bm) be a finite family of ■(μ) functions. In this paper, some weak-type multiple weighted estimates for the iterated commutator ■Tgenerated by T and ■ are obtained.     

A local version of Hardy spaces associated with operators on metric spaces

Let(X,d,μ) be a metric measure space endowed with a distance d and a nonnegative Borel doubling measure μ.Let L be a second order self-adjoint positive operator on L2(X).Assume that the semigroup e tL generated by L satisfies the Gaussian upper bounds on L 2(X).In this article we study a local version of Hardy space h1L(X) associated with L in terms of the area function characterization,and prove their atomic characters.Furthermore,we introduce a Moser type local boundedness condition for L,and then we apply this condition to show that the space h1L(X) can be characterized in terms of the Littlewood-Paley function.Finally,a broad class of applications of these results is described.     

THE CONVERGENCE RATES OF ASYMPTOTICALLY BAYES DISCRIMINATION

§1. Introduction and Main Results Let (X, θ), (X_1, θ_1), ..., (X_n, θ_n) be R~d×{0, 1} valued independent identically distributed (iid) random variables (r. v.), with P(θ=1)=p_1 and P(θ=0)=p_0=1-p_1. Let the conditional density function of X given θ=i be f_i(x)dx, i=0, 1. (X_1, θ_1),..., (X_n, θ_n) are known     

Two examples on atomic doubling measures

It is shown that there is a compact set X⊂[0,1] with dimHX=1 on which all doubling measures are purely atomic. It is also shown that there is a compact set X⊂[0,1] with a dense set of isolated points and dimHX=0 on which no doubling measures are purely atomic.     

The Space of Simple Configurations is Polish

It is proved that the space of configurations without multiple points on a smooth Riemannian manifold is Polish with respect to the weak topology; a criterion for a subspace of this space to be precompact is given.     

符号空间有限型子转移混沌集的Hausdorff测度与Parry测度

设A是一个每列至少有二个元素为1的不可约0，1方阵，(∑4，σA)为由A所决定的符号空间有限型子转移．在∑A上定义一个与其拓扑相容的度量d使得(∑A，d)的Hausdorff维数为1．若G是H^-可测的σA的Li—Yorke混沌集，则H^1(C)＝0；若A是本原的，则存在一个σA的有限型混沌集S使得H^1(S)＝1，其中H^1为1-维的Hausdorff测度．     

Computability of measurable sets via effective metrics

We consider how to represent the measurable sets in an infinite measure space. We use sequences of simple measurable sets converging under metrics to represent general measurable sets. Then we study the computability of the measure and the set operators of measurable sets with respect to such representations. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Strong mixing subshift of finite type and Hausdorff measure of its chaotic set

We present a sufficient and necessary condition for the subshift of finite type to be a measure-preserving transformation or to be a strong mixing measure-preserving transformation with respect to the Hausdorff measure. It is proved that a strong mixing subshift of finite type has a chaotic set with full Hausdorff measure.     

Two fixed-point theorems

Two fixed point theorems implementing a more general principle for partially ordered sets (which is also due to this author) are proved. Translated fromMatematicheskie Zametki, Vol. 66, No. 6, pp. 920–923, December, 1999.     

Harmonic calculus on fractals--A measure geometric approach II

Riesz potentials of fractal measures in metric spaces and their inverses are introduced. They define self-adjoint operators in the Hilbert space and the former are shown to be compact.

In the Euclidean case the corresponding spectral asymptotics are derived with Besov space methods. The inverses of the Riesz potentials are fractal pseudodifferential operators. For the order two operator the spectral dimension coincides with the Hausdorff dimension of the underlying fractal.

     

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.     

Ahlfors 正则空间上的开集分解与加倍测度

对于一致完全的加倍度量空间建立了 Whitney 分解定理. 作为应用, 借助于 Ahlfors 正则空间上的加倍测度描述了它的任意非空闭集的 Whitney 修正集上的加倍测度.     

有界闭凸值测度的集值积分

引入实值函数关于有界闭凸值测度的集值积分,并讨论了集值积分的收敛定理,证明了当集值测度为有界闭凸集值的有界变差集值测度时,关于弱紧凸集值测度的积分性质对有界闭凸集值测度仍然保持.推广了实值函数关于弱紧凸值测度的积分.