关于Campanato空间的一个注记

类似于Campanato空间理论，本文对具有以下连续模的函数类给出了一局部积分刻画：｜u（x）-u（y）｜≤C｜x—y｜^α（log｜x—y｜^-1）β，z，y∈Ω，其中C〉0，Ω为R^d中一正则区域，α∈（0，1]，β∈[0，1]．     

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.     

A Note on Hilbert Algebras and Their Related Generalized Esakia Spaces

Generalized Esakia spaces are the topological duals of bounded implicative semilattices in the duality studied by G. Bezhanishvili and R. Jansana. We study the relation between a Hilbert algebra and the generalized Esakia space dual to its free implicative semilattice extension. To establish the relation we introduce a category whose objects are a generalized Esakia space together with a family of clopen up-sets that constitutes a subalgebra of the implication fragment of the Heyting algebra of the up-sets of the generalized Esakia space.     

随机度量空间及其应用

首先证明取值于度量空间(可分或不可分)的随机元可构成随机度量空间;取值于赋范空间的随机元可嵌入到随机赋范空间中.接着给出这些结论对随机算子的应用.最后统一给出赋范空间上几乎处处有界的随机线性泛函的表示.     

齐型空间上的Herz空间及其应用

定义了一类齐型空间上的Herz空间及弱Herz空间,研究了定义在这些空间中的一类次线性算子的性质．     

Composition Operators Between Analytic Campanato Spaces

This note characterizes both boundedness and compactness of a composition operator between any two analytic Campanato spaces on the unit complex disk.     

Hausdorff算子在Campanato空间的有界性

研究了几种不同类型的Hausdorff算子在Campanato空间的有界性,并且得到了这些算子在Campanato空间上有界的最佳常数.此外,还讨论了多线性Hausdorff算子在Morrey空间中的有界性.     

A Note on Sobolev Spaces

In the theory of averaging and other branches of mathematical physics, a crucial role is played by Sobolev spaces connected with a Borel measure defined in the Euclidean space ℝ^d. These spaces are defined as closures of the sets of smooth functions in an appropriate norm. In this paper, we propose another (dual) definition of Sobolev spaces and give an example of using this definition.__________Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 10, Suzdal Conference-4, 2003.     

关于sn度量空间的注记

The main purpose of this paper is to establish the mapping relation between metric spaces and sn-metric spaces.     

广义Campanato空间上粗糙核参数型Marcinkiewicz积分

作为一类Littlewood-Paley函数,μ_(Ω,b)~ρ(f)是带非齐次粗糙核的参数型Marcinkiewicz积分,其中粗糙核Ω∈L~q(S~(n-1))满足消失性和积分Dini连续,径向核b∈Δ_s(R~+)∩Θ_s(R~n),1q,s∞,复参数ρ具有正实部.仅在一点有限的假设下,该文建立了μ_(Ω,b)~ρ(f)在广义Campanato空间L~(p,φ)(R~n)上的存在性和有界性,本质地推进了众多的已有工作.     

$c$-半层空间与几乎完全正则空间一点注记

In this paper, we give some characterizations of almost completely regular spaces and c-semistratifiable spaces(CSS) by semi-continuous functions. We mainly show that:(1)Let X be a space. Then the following statements are equivalent:(i) X is almost completely regular.(ii) Every two disjoint subsets of X, one of which is compact and the other is regular closed, are completely separated.(iii) If g, h : X → I, g is compact-like, h is normal lower semicontinuous, and g ≤ h, then there exists a continuous function f : X → I such that g ≤ f ≤ h;and(2) Let X be a space. Then the following statements are equivalent:(a) X is CSS;(b) There is an operator U assigning to a decreasing sequence of compact sets(Fj)j∈N,a decreasing sequence of open sets(U(n,(Fj)))n∈N such that(b1) Fn■U(n,(Fj)) for each n ∈ N;(b2)∩n∈NU(n,(Fj)) =∩n∈NFn;(b3) Given two decreasing sequences of compact sets(Fj)j∈N and(Ej)j∈N such that Fn■Enfor each n ∈ N, then U(n,(Fj))■U(n,(Ej)) for each n ∈ N;(c) There is an operator Φ : LCL(X, I) → USC(X, I) such that, for any h ∈ LCL(X, I),0 Φ(h) h, and 0 Φ(h)(x) h(x) whenever h(x) 0.     

关于超一致空间的一个注记

最近,张德学引入了拓扑构造的co-tower扩张这一概念,并证明了不分明拓扑学中若干熟知的范畴构造可以表示为较为简单的范畴构造的co-tower扩张.本文证明了由J.GutiérrezGarcía和M.A.dePradaVicente[3]引入的超一致空间构造SUS具体同构与R.Lowen[9]意义下的不分明一致空间构造FUS的cco-tower扩张的一个满子构造,而已知FUS同构于一致空间构造的co-tower扩张.     

A Note on Partial b-Metric Spaces

Mediterranean Journal of Mathematics - Let (X,b) be a partial b-metric space with coefficient $${s geq 1. ,,{rm For ,, each},, x in X ,,{rm and ,,each},, varepsilon > 0,...     

关于单调亚紧空间

In the first part of this note, we mainly prove that monotone metacompactness is hereditary with respect to closed subspaces and open Fó-subspaces. For a generalized ordered (GO)-space X, we also show that X is monotonically metacompact if and only if its closed linearly ordered extension X* is monotonically metacompact. We also point out that every non-Archimedean space X is monotonically ultraparacompact. In the second part of this note, we give an alternate proof of the result that McAuley space is paracompact and metacompact.     

Weighted Multi-Parameter Mixed Hardy Spaces and Their Applications

Czechoslovak Mathematical Journal - Applying discrete Calderón’s identity, we study weighted multi-parameter mixed Hardy space $$H_{{rm{mix}}}^p(omega ,{mathbb{R}^{{n_1}}} times...     

近似空间的拓扑性质及其应用

近似空间(U,R)的全体可定义集构成X上的一个拓扑.本文在不要求论域U是有限的前提下探讨近似空间上这个拓扑的局部性质和可数性质,以及拓扑空间可近似化的充要条件及公理化体系,并寻找它们在粗糙集理论中的应用.     

概率赋范空间上的一些不动点定理的进一步分析

该文在局部有界ＰＮ空间或邻域卜局部凸ＰＮ空间上,证明了非空完备子集上的概率压缩映象必有唯一不动点;并在度量线性空间中给出了关于伪范族一致压缩映象的不动点定理．     

A Note on Isomorphic Groups and Nonhomeomorphic Spaces

Given a Tychonov space X we can construct another space Y with the same group of homeomorphisms such that X and Y are, in some sense, "almost arbitrarily different".