New characterizations of Hajlasz-Sobolev spaces on metric spaces

This paper introduces the fractional Sobolev spaces on spaces of homogeneous type,includingmetric spaces and fractals. These Sobolev spaces include the well-known Hajfasz-Sobolev spaces as specialmodels.The author establishes varions chaaracterizations of(sharp)maximal functions for these spaces.Asapplications,the author identifies the fractional Sobolev spaces with some Lipscitz-type spaces.Moreover;some embedding theorems are also given.     

Interpolation on weak martingale Hardy space

By the weak atomic decompositions of weak martingale Hardy spaces, we investigate the interpolation spaces between weak martingale Hardy spaces and martingale Hardy spaces.     

取值于序拓扑向量空间的映射与层空间

In the paper [Monotone countable paracompactness and maps to ordered topological vector spaces, Top. Appl., 2014, 169(3): 51–70], Yamazaki initiated the study on maps with values into ordered topological vector spaces. Characterizations of monotonically countably paracompact spaces and some other spaces in terms of maps to ordered topological vector spaces were obtained. In this paper, following Yamazaki's method, we present some characterizations of stratifiable spaces and k-semi-stratifiable spaces in terms of maps with values into ordered topological vector spaces.     

On σ-images of Metric Spaces

In this paper the relation between the σ-images of metrical spaces and spaces with σ-locally finite cs-network, or spaces with σ-locally finite cs^*-network, or spaces with σ-locally finite sequence neighborhood network, or spaces with σ-locally finite sequence open network are established by use of σ-mapping.     

Characterizations of Sobolev spaces in Euclidean spaces and Heisenberg groups

Recently, many new features of Sobolev spaces W k,p ？RN ？ were studied in [4-6, 32]. This paper is devoted to giving a brief review of some known characterizations of Sobolev spaces in Euclidean spaces and describing our recent study of new characterizations of Sobolev spaces on both Heisenberg groups and Euclidean spaces obtained in [12] and [13] and outlining their proofs. Our results extend those characterizations of first order Sobolev spaces in [32] to the Heisenberg group setting. Moreover, our theorems also provide diff erent characterizations for the second order Sobolev spaces in Euclidean spaces from those in [4, 5].     

关于某些广义可数紧空间

We first give alternative expressions of some generalized countably compact spaces such as quasi-γ spaces, quasi-Nagata spaces, M#-spaces and wM-spaces with g-functions. Then by means of these expressions, we present some characterizations of the corresponding spaces with real-valued functions.     

Variable Besov-type Spaces

In this paper we introduce Besov-type spaces with variable smoothness and integrability.We show that these spaces are characterized by the φ-transforms in appropriate sequence spaces and we obtain atomic decompositions for these spaces.Moreover the Sobolev embeddings for these function spaces are obtained.     

CBMO estimates for multilinear Hardy operators

The purpose of this paper is to study the multilinear Hardy operators in higher dimensional cases and establish the CBMO estimates for multilinear Hardy operators on some function spaces, such as the Lebesgue spaces, the Herz spaces and the Morrey-Herz spaces.     

BERGMAN TYPE PROJECTIONS ON L~p SPACES

The paper is a survey on the action of Bergman type projections on various Lp spaces. The focus is on three types of holomorphic function spaces: weighted Bergman spaces, the Block space, and diagonal Besov spaces.     

BERGMAN TYPE PROJECTIONS ON L^p SPACES

The paper is a survey on the action of Bergman type projections on various Lp on three types of holomorphic function spaces： weighted Bergman spaces, the Bloch spaces. The focus is space, and diagonal Besov spaces.     

SYNTOPOFORMIC SPACES (SYNTOPOGENOUS LIMIT SPACES)

Abstract

Császár generalized the uniform spaces, the proximity spaces and the topological spaces to syntopogenous spaces. Cook and Fischer generalized the uniform spaces to uniform limit spaces. Finally Marny generalized the proximity spaces to proximal limit spaces. Analogously we generalize the syntopogenous spaces to syntopoformic spaces (syntopogenous limit spaces). These spaces include all the above mentioned in a suitable sense. We extend some of the well-known results of compactness and completeness to syntopoformic spaces.     

小波与函数空间

Triebe利用Littlewood Paley分解将大多数函数空间分类成两类三指标的函数空间：Besov空间和Triebel Lizorkin空间；但Littlewood Paley 分解很难直接分析Sobolev空间L^p的插值空间Lorentz空间，也很难分析Triebel Lizorkin空间F^{α,q}_1的预备对偶空间和对偶空间.运用小波，作者给出这些空间一个统一刻画：Triebel Lizorkin Lorentz 空间，Besov Lorentz空间和F^{α,q}_1的预备对偶空间和对偶空间；另外也研究这些空间的三个性质.     

随机结构空间理论初探

提出了随机结构空间的概念，引出了随机拓扑空间、随机度量空间、随机赋范空间、随机内积空间、随机关系等随机数学结构的概念，初步研究了随机度量空间、随机赋范空间、随机内积空间的基本构造以及与概率度量空间、概率赋范空间、概率内积空间的关系。     

Uniformity Structures on L-Fuzzy Spaces

We extend the notion of a uniform space in a natural way by defining a uniform spaces in L-fuzzy spaces.Although these spaces seem quite similar to ordinary case,we show that the category of this uniform spaces is a good extension of the category of ordinary uniform spaces and the category of L-uniform spaces.Moreover,we introduce the concept of uniform topological spaces in the framework of uniform spaces in L-fuzzy spaces.Furthermore,the relation between proximity and uniform spaces in L-fuzzy spaces will...     

Fuzzy φψ-continuous Functions between L-topological Spaces (Ⅱ)

In the present paper, sum operation on sum spaces of a family of L-topological spaces is defined. Fuzzy φψ-continuity from sum spaces of a family of L-topological spaces into L-product spaces and from sum spaces of a family of L-topological spaces into L-topological spaces are investigated.     

Characterization of inner product spaces in V- and L-spaces

In [4], Freese and Murphy introduce a new class of spaces, the V-spaces, which include Banach spaces, hyperbolic spaces, and other metric spaces. In this class of spaces they investigate conditions which are equivalent to strict convexity in Banach spaces, and extend some of the Banach space results to this new class of spaces. It is natural to ask if known characterizations of real inner product spaces among Banach spaces can also be extended to this larger class of spaces. In the present paper it will be shown that a metrization of an angle bisector property used in [3] to characterize real inner product spaces among Banach spaces also characterizes real inner product spaces among V-spaces, and among another class of spaces, the L-spaces, which include hyperbolic spaces and strictly convex Banach spaces. In the process it is shown that in a complete, convex, externally convex metric space M, if the foot of a point on a metric line is unique, then M satisfies the monotone property, thus answering a question raised in [4].     

p-进中心函数空间及奇异积分算子

引入了几类p-中心函数空间,包括p进A~q和B~q空间、p进λ-中心BMO空间以及p-进中心Morrey空间,得到了p-进A~q空间与B~q空间的对偶性、p-进λ-中心BMO空间和中心Morrey空间的特征,研究了这些空间与加权p-进Lebesgue空间之间的关系.另外,还建立了一类奇异积分算子在p-进中心Morrey空间中的有界性,更进一步,得到了这类算子交换子在p-进中心Morrey空间中的λ-中心BMO估计.     

A Generalization of Probabilistic Uniform Spaces

We develop a theory for probabilistic semiuniform convergence spaces. Probabilistic semiuniform convergence spaces generalize probabilistic uniform spaces in the sense of Florescu and probabilistic convergence spaces in the sense of Kent and Richardson. This theory includes a new branch in topology, namely, Convenient Topology, introduced by Preuß. Thus, it includes semiuniform convergence spaces and uniform spaces, filter and Cauchy spaces and (symmetric) limit spaces and, therefore, (symmetric) topological spaces. The theory of probabilistic semiuniform convergence spaces reveals categories which are strong topological universes or have other convenient properties.     

Lorentz序列空间的装球问题

Ｂａｎａｃｈ空间中装球问题的研究，近四十年来已取得了令人瞩目的发展。Ｂａｎａｃｈ空间的装球值的范围已经确定，Ｌ＿ｐ空间及Ｏｒｌｉｃｚ序列空间Ｉ＿Ｍ等许多经典Ｂａｎａｃｈ空间装球值已经找到．本文研究又一类经典Ｂａｎａｃｈ空间──Ｌｏｒｅｎｔｚ序列空间的装球问题，给出了Ｌｏｒｅｎｔｚ序列空间的装球值。