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.     

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].     

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.     

Generalization of the notion of grand Lebesgue space

We introduce families of weighted grand Lebesgue spaces which generalize weighted grand Lebesgue spaces (known also as Iwaniec-Sbordone spaces). The generalization admits a possibility of expanding usual (weighted) Lebesgue spaces to grand spaces by various ways by means of additional functional parameter. For such generalized grand spaces we prove a theorem on the boundedness of linear operators under the information of their boundedness in ordinary weighted Lebesgue spaces. By means of this theorem we prove boundedness of the Hardy-Littlewood maximal operator and the Calderon-Zygmund singular operators in the weighted grand spaces.     

Abstract capacitary estimates and the completeness and separability of certain classes of non-locally convex topological vector spaces

We are concerned with establishing completeness and separability criteria for large classes of topological vector spaces which are typically non-locally convex, including Lebesgue-like spaces, Lorentz spaces, Orlicz spaces, mixed-normed spaces, tent spaces, and discrete Triebel–Lizorkin and Besov spaces. For vector spaces of measurable functions we also derive pointwise convergence results. Our approach relies on abstract capacitary estimates and works in certain cases of interest even in the absence of a background measure space and/or of a vector space structure.     

Completion of Semiuniform Convergence Spaces

Semiuniform convergence spaces form a common generalization of filter spaces (including symmetric convergence spaces [and thus symmetric topological spaces] as well as Cauchy spaces) and uniform limit spaces (including uniform spaces) with many convenient properties such as cartesian closedness, hereditariness and the fact that products of quotients are quotients. Here, for each semiuniform convergence space a completion is constructed, called the simple completion. This one generalizes Császár's -completion of filter spaces. Thus, filter spaces are characterized as subspaces of convergence spaces. Furthermore, Wyler's completion of separated uniform limit spaces can be easily derived from the simple completion.     

Uniform universal covers of uniform spaces

We develop a generalized covering space theory for a class of uniform spaces called coverable spaces. Coverable spaces include all geodesic metric spaces, connected and locally pathwise connected compact topological spaces, in particular Peano continua, as well as more pathological spaces like the topologist's sine curve. The uniform universal cover of a coverable space is a kind of generalized cover with universal and lifting properties in the category of uniform spaces and uniformly continuous mappings. Associated with the uniform universal cover is a functorial uniform space invariant called the deck group, which is related to the classical fundamental group by a natural homomorphism. We obtain some specific results for one-dimensional spaces.     

关于GB型空间的若干结果

本文对GB型空间进行了若干讨论,得到了一些结果。 设X为Banach空间,X为X的共轭空间,B(X,X)为X到X的所有有界线性算子组成的空间。如果X中的弱收敛序列为弱收敛序列,则称X为GB型空间。Grothendieck.A于1953年证明了l~∞是GB型空间。显然自反空间是GB型空间。     

k半层空间的性质及相关问题

k半层空间是层空间与N空间的共同推广,本文综述k半层空间的研究进展,介绍k半层空间的刻画、性质及其推广,给出一些相关问题,供进一步研究.     

Characterizations of certain classes of infinite-dimensional metric spaces

We characterize two classes of metric spaces as images under a closed, finite-to-one mapping of a zero-dimensional metric space. In the case of locally finite-dimensional spaces the mapping must be of strong local order, and for strongly countable-dimensional spaces the mapping must have weak local order. The results are analogues to characterizations by K. Morita (of finite-dimensional spaces) and J. Nagata (of countable-dimensional spaces).     

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...     

Inclusion properties of generalized Morrey spaces

This paper discusses the structure of Morrey spaces, weak Morrey spaces, generalized Morrey spaces, and generalized weak Morrey spaces. Some necessary and sufficient conditions for the inclusion property of these spaces are obtained through a norm estimate for the characteristic functions of balls.     

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.     

Altitude properties and characterizations of inner product spaces

New characterizations of real inner product spaces (euclidean spaces) among metric spaces are obtained from familiar formulas expressing the altitude (height) of a triangle as a function of the lengths of its sides. Other properties related to the altitude of a triangle are also shown to result in characterizations of euclidean spaces, or euclidean and hyperbolic spaces.     

On quasilinear spaces of convex bodies and intervals

Algebraic systems abstracting properties of convex bodies and intervals, with respect to addition and multiplication by scalars, known as quasilinear spaces, are studied axiomatically. We discuss special quasilinear spaces with group structure called quasivector spaces. We show that every quasivector space is a direct sum of a vector space and a symmetric quasivector space. A complete characterization of symmetric quasivector spaces in the finite dimensional case is given, which permits to reduce computation in quasilinear spaces to computation in familiar vector spaces.     

On the classification of weakly symmetric Finsler spaces

In this paper, we give the classification of some special types of weakly symmetric Finsler spaces. We first present a general principle to classify weakly symmetric Finsler spaces and also give a method to figure out the Berwald spaces among the class of weakly symmetric Finsler spaces. Then we give an explicit classification of weakly symmetric Finsler spaces with reductive isometric groups as well as the left invariant weakly symmetric Finsler metrics on nilpotent Lie groups of the Heisenberg type. As an application, we obtain a large number of high-dimensional examples of reversible Finsler spaces which are non-Berwaldian and with vanishing S-curvature, a kind of spaces which are sought after in an open problem of Z. Shen.     

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。     

Preduals of Campanato Spaces and Sobolev-Campanato Spaces: A General Construction

In this paper we describe two limiting processes for families of Banach spaces closely related to the standard definition of projective and inductive limits. These processes lead again to Banach spaces. Information about linear operators and duality between basic families of spaces is carried over to the corresponding limit spaces. The abstract results are shown to be applicable to Campanato spaces and Sobolev-Campanato spaces. In particular, we obtain the existence and a characterization of predual spaces. Some imbedding relations are investigated in more detail.     

Weak additivity of metric pythagorean orthogonality

It is well known that the property of additivity of pythagorean orthogonality characterizes real inner product spaces among normed linear spaces. In the present paper, a natural concept of additivity is introduced in metric spaces, and it is shown that a weakened version of this additivity of metric pythagorean orthogonality characterizes real inner product spaces among complete, convex, externally convex metric spaces, providing a generalization of the earlier characterization.     

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.