Banach-Saks property in Marcinkiewicz spaces

We catalogue all Marcinkiewicz function and sequence spaces with the Banach-Saks property and present necessary and sufficient conditions for a wide subclass of spaces to possess the p-Banach-Saks property, 1<p<∞. We apply our results to several open problems.     

混合范数空间中函数的Taylor系数

本文研究了混合范数空间Ｈ（ｐ，ｑ，ａ）中解析函数ｆ的Ｔａｙｌｏｒ系数，对０＜ｐ≤２，０＜ｑ＜∞，ａ＞０和２≤ｐ＜∞，０＜ｑ＜∞，ａ＞０两种情形，分别给出了ｆ属于Ｈ（ｐ，ｑ，ａ）的必要条件和充分条件。用上述结果我们还得到了几个关于混合范数空间的乘子定理，这些结果也推广了Ｈａｒｄｙ和Ｌｉｔｔｌｅｗｏｏｄ关于Ｈ＾ｐ空间的相应结论。     

A Fixed Point Theorem in Intuitionistic Fuzzy Metric Spaces by Using New Commutativity Condition

We prove a common fixed point theorem for discontinuous,noncompatible mappings on noncomplete intuitionistic fuzzy metric spaces by using a new commutativity condition.We validate our main result by an example.     

Holomorphic Dependence of the Heins Map

Let D be a bounded convex domain and Hol _c (D,D) the set of holomorphic maps from D to C ⁿ with image relatively compact in D. Consider Hol _c (D,D) as a open set in the complex Banach space H ^∞ _n (D) of bounded holomorphic maps from D to C ⁿ . We show that the map τ: Hol _c (D,D) → D (called the Heins map for D equals to the unit disc of C) which associates to ? ∈ Hol _c (D,D) its unique fixed point τ? ∈ D is holomorphic and its differential is given by dτ_?(v) = (Id-df_τ(?))^?1 v(τ(?)) for v ∈ H ^∞ _n (D).     

一类非线性算子的带误差的Ishikawa迭代程序及其稳定性

建立了任意实Banach空间中带误差的Ishikawa迭代程序逼近Lipschitz强伪压缩算子的不动点的一般性定理,指出已被广泛广泛研究的Ishikawa迭代序列的稳定性问题仅是带误差的Ishikawa迭代程序的特例,作为直接的应用,用不同于通常的方法证得任意实Banach空间中的Ishikawa迭代序列关于Lipschitz强伪压缩算子是稳定的,这些推广或发展了近期许多相应的结果。     

Discrete Calderón-type Reproducing Formula

In this paper we use the Calderón-Zygmund operator theory to provide a discrete Calderón-type reproducing formula. Since translation, dilation and, in particular, the Fourier transform are never used in the proofs, all results still hold on spaces of homogenous type introduced by Coifman and Weiss. As a consequence, we obtain a class of frames with the minimum regularity properties. Received: July 27, 1999, Accepted: October 15, 1999     

Introduction to Hardy Spaces

Basic material from the theory of Hardy spaces is presented. The principle of positive energy representations is used as motivation to introduce these spaces.     

粒度空间约简及其粗糙集模型研究

针对交可约粒度空间中覆盖、基和粒结构的关系,结合偏序关系的哈斯图,给出一种约简粒度空间的方法.另外,通过限定上、下近似算子的取值范围,重新定义了交可约粒度空间上的粗糙集模型,并讨论了其相关性质.     

Littlewood-Paley算子交换子在加权Herz型Hardy空间上的有界性

研究了Littlewood-Paley算子交换子gψ,b在加权Herz型Hardy空间上的性质,并证明了gψ,b在某些条件下是HKa,pq(ω1,ω2)到Ka,pq(ω1,ω2)和HKa,pq(ω1,ω2)到WKa,pq(ω1,ω2)上的有界算子.     

Morgan-Scott剖分上样条空间S_8~4(Δ_(ms))的维数

Ｍｏｒｇｅｎ－Ｓｃｏｔ剖分上样条空间的维数依赖于剖分的几何性质，本文证明了Ｄｉｅｎｅｒ１９９０年提出的猜想对ｒ＝４是不正确的，需要修正．