序列位差空间的拓扑性质

利用拓扑学的一般理论,研究了序列位差空间的连通性,给出了序列位差空间为可分空间、紧致空间的充分必要条件.     

超积空间及其性质

引进了和内积空间没有相互包含关系的一类新空间:超积空间,进而研究了超积空间的性质.这类新的线性空间具有许多内积空间的重要性质,从而得到了线性空间一类新的度量刻画.     

关于G-M成果研究的若干新动态Ⅰ——G-M型空间的若干品种

结合自己的工作，对Gowers-Maurey系列成果获Fields奖以来的研究的新动态作一综述。本是上篇，主要讨论含遗传不可分解空间在内的G－M型空间的若干品种。     

A characterization of Bloch space and Besov space

On the unit disk of the complex plane, a characterization for the membership of Bloch space and analytic Besov space is expressed extending known results.     

The behaviour on the rays of functions from the Bergman and Fock spaces

In this note we study the behaviour of holomorphic functions from the Bergman and Fock spaces on the rays of the unit disc U and the complex plane ℂ. We obtain conditions on the finiteness of weighted L ²-integrals of those functions along rays.      

C~n中单位球上一些全纯函数空间的刻画

本文讨论了多复变中混合赋范空间、Dirichlet型空间、Bloch型空间等全纯函数空间的一些等价刻画,获得了一系列充要条件.     

Stein domains in Banach algebraic geometry

In this article we give a homological characterization of the topology of Stein spaces over any valued base field. In particular, when working over the field of complex numbers, we obtain a characterization of the usual Euclidean (transcendental) topology of complex analytic spaces. For non-Archimedean base fields the topology we characterize coincides with the topology of the Berkovich analytic space associated to a non-Archimedean Stein algebra. Because the characterization we used is borrowed from a definition in derived geometry, this work should be read as a derived perspective on analytic geometry.     

On the resolvability of locally connected spaces

We solve a problem of Padmavally about resolvability of locally connected spaces, in the case where the space under consideration is regular.

     

The product of a Baire space with a hereditarily Baire metric space is Baire

In this paper we prove that the product of a Baire space with a metrizable hereditarily Baire space is again a Baire space. This answers a recent question of J. Chaber and R. Pol.

     

Weight generalization of the space of continuous functions vanishing at infinity

In this paper, we characterize the weighted generalization of the space of continuous functions vanishing at infinity and correct some wrong results in the paper. Let X be a locally compact space and ν is an arbitrary weight (non-negative function) on X. We give a correct and comprehensive definition of the weighted generalization $C_0^{\nu }(X)$ of $C_0(X)$, and show that it is a seminormed space with respect to the canonical seminorm ${\parallel f\parallel }_{\nu }={sup}_{x\in X}|f(x)|$, where $f\in C_0^{\nu }(X)$. We find conditions on ν under which $C_0^{\nu }(X)$, with respect to ${\parallel .\parallel }_{\nu }$, becomes a normed space or a Banach space or an algebra, or a topological algebra, respectively.     

Metrically generated theories

Many examples are known of natural functors describing the transition from categories of generalized metric spaces to the ``metrizable" objects in some given topological construct . If preserves initial morphisms and if is initially dense in , then we say that is -metrically generated. Our main theorem proves that is -metrically generated if and only if can be isomorphically described as a concretely coreflective subconstruct of a model category with objects sets structured by collections of generalized metrics in and natural morphisms. This theorem allows for a unifying treatment of many well-known and varied theories. Moreover, via suitable comparison functors, the various relationships between these theories are studied.

     

几个l~0类赋准范空间的共轭空间的表示定理

讨论赋准范空间的共轭空间的表示问题,研究几个l~0类赋准范空间的共轭空间的表示定理,得到代数表示连等式(l~0)~*(A=)(c~0)~*(A=)(c_0~0)~*(A=)(c_(00)~0)~*(A=)c_(00),与拓扑表示定理((c_(00)~0)~*,sw~*)=c_(00)~0.     

Characterizations of Function Spaces via Boundedness of Commutators

In this paper, we give some creative characterizations of Campanato spaces via the boundedness of commutators associated with the Calder ′on-Zygmund singular integral operator, fractional integrals and Hardy type operators. Furthermore, we put forward a few problems on the characterizations of Campanato type spaces via the boundedness of commutators.     

Lipschitz estimates for multilinear commutator of Littlewood-Paley operator

In this paper, we will study the continuity of multilinear commutator generated by Littlewood-Paley operator and Lipschitz functions on Triebel-Lizorkin space, Hardy space and Herz-Hardy space.      

First countable extensions of regular spaces

We investigate feebly compact extensions of first countable regular locally feebly compact spaces. Solutions of problems posed by R. M. Stephenson, Jr. and G. M. Reed are given.

     

Boundedness of Fractional Integrals with a Rough Kernel on the Pro duct Triebel-Lizorkin Spaces

By using the Littlewood-Paley decomposition and the interpolation the-ory, we prove the boundedness of fractional integral on the product Triebel-Lizorkin spaces with a rough kernel related to the product block spaces.     

On geodesic mappings of equidistant generalized Riemannian spaces

In this paper geodesic mappings of equidistant generalized Riemannian spaces are discussed. It is proved that each equidistant generalized Riemannian space of basic type admits non-trivial geodesic mapping with preserved equidistant congruence. Especially, there exists non-trivial geodesic mapping of equidistant generalized Riemannian space onto equidistant Riemannian space. An example of geodesic mapping of an equidistant generalized Riemannian spaces is presented.     

On van Mill's example of a normed

In 1987 van Mill constructed an infinite-dimensional normed space which is not homeomorphic with the product . We give a short proof of this property of van Mill's example.

     

Boundedness of commutators on Hardy type spaces

Let [b, T] be the commutator of the function b ∈ Lipβ(Rn) (0 ＜β≤ 1) and the CalderónZygmund singular integral operator T. The authors study the boundedness properties of [b, T] on the classical Hardy spaces and the Herz-type Hardy spaces in non-extreme cases. For the boundedness of these commutators in extreme cases, some characterizations are also given. Moreover, the authors prove that these commutators are bounded from Hardy type spaces to the weak Lebesgue or Herz spaces in extreme cases.