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Stone's representation theorem in fuzzy topology

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Science China Mathematics 2003年第6期46卷 775-788页

作者：刘应明张德学 Department of Mathematics Sichuan University Chengdu 610064 China Correspondence should be addressed to Liu Yingming

In this paper, a complete solution to the problem of Stone's repesentation theorem in fuzzy topology is given for a class of completely distributive lattices. Precisely, it is proved that if L is a frame such that 0 ∈ L is a prime or 1 ∈ L is a coprime, then the category of distributive lattices is dually equivalent to the category of coherent L-locales and that if L is moreover completely distributive, then the category of distributive lattices is dually equivalent to the category of coherent stratified L-topological spaces.

关键词： distributive lattice, L-topological space, Stone's representation theorem, frame.

On mapping degrees between 1-connected 5-manifolds

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Science China Mathematics 2006年第12期49卷 1855-1863页

作者： TAN Liang LMAM Department of MathematicsPeking UniversityBeijing 100871China

We study the set of the mapping degrees between simply connected closed manifolds in this paper.

关键词： mapping degree,simply connected manifolds,Moore space,

Boundedness of Marcinkiewicz integrals and their commutators in H^1(R^n×R^m)

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Science China Mathematics 2006年第6期49卷 770-790页

作者： YANG Dachun ZHOU Yuan School of Mathematical Sciences Beijing Normal University Beijing 100875 China School of Mathematical Sciences Beijing Normal University Beijing 100875 China

The authors establish the boundedness of Marcinkiewicz integrals from the Hardy space H1(Rn × Rm) to the Lebesgue space L1(Rn × Rm) and their commutators with Lipschitz functions from the Hardy space H1(Rn × Rm) to... 详细信息

关键词： Marcinkiewicz integral, commutator, Lipschitz function, atom, Hardy space,Lebesgue space, boundedness.

An approximation problem of the finite rank operator in Banach spaces

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Science China Mathematics 2003年第2期46卷 245-250页

作者：王玉文潘少荣 Department of Mathematics Harbin Normal University

By the method of geometry of Banach spaces, we have proven that a bounded linear operatorin Banach space is a compact linear one iff it can be uniformly approximated by a sequence of the finite rankbounded homogeneous... 详细信息

关键词： Banach space, compact linear operator, bounded homogeneous operator, finite rank operator, approximation.

On concretely both reflective and coreflective subconstructs of Chang fuzzy topological spaces

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Science China Mathematics 2003年第1期46卷 107-117页

作者：张德学 Department of Mathematics Sichuan University

In this paper, the concretely both reflective and coreflective subconstructs of the construct CFTSof Chang fuzzy topological spaces are characterized and their relationship to such subconstructs of stratifiedfuzzy topological spaces is investigated. Properties of a particular such subconstruct of CFTS, the constructof weak fuzzy neighborhood spaces, are discussed in detail. And it is proved that there exists exactly c suchsubconstructs between the subconstruct of weakly induced spaces and CFTS.

关键词： fuzzy topological space, topological constructs, reflective and coreflective subcon-structs, total fuzzy topology.

The Gleason's problem on mixed norm spaces in convex domains

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Science China Mathematics 2003年第6期46卷 827-837页

作者：胡璋剑 Department of Mathematics Huzhou Teachers College Huzhou 313000 China Let Ωbe a bounded convex domain with C2 boundary in C2 and for given 0 < p q ≤∞and normal weight function (r) let Hpq be the mixed norm space on Ω. In this paper we prove that the Gleason's problem (Ω a Hpq) is solvable for any fixed point a ∈Ω. While solving the Gleason's problem we obtain the boundedness of certain integral operator on Hpq.

Let Ω be a bounded convex domain with C2 boundary in Cn and for given 0 ＜ p, q ≤∞ and normal weight function ψ(r) let Hp,q,ψ be the mixed norm space on Ω. In this paper we prove that the Gleason's problem (Ω, a, Hp,q,ψ) is solvable for any fixed point a ∈Ω. While solving the Gleason's problem we obtain the boundedness of certain integral operator on H-p,q,ψ.

关键词： Gleason's problem, mixed norm space, normal weight.

Invariant subspaces for sequentially subdecomposable operators

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Science China Mathematics 2003年第4期46卷 433-439页

作者：刘明学 Institute of Mathematics Changsha UniversityChangsha 410003 China

In this paper, using Brown technique, we prove the Mohebi-Radjabalipour Conjecture by strengthening a slight thickness condition of the spectrum, and obtain some invariant subspace theorems. Our result contains an imp... 详细信息

关键词： Banach space, sequentially subdecomposable operators, invariant subspace.

New characterizations of Hajlasz-Sobolev spaces on metric spaces

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Science China Mathematics 2003年第5期46卷 675-689页

作者：杨大春 Department of Mathematics. Beijing Normal University Beijing 100875 China

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 various characterizations 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.

关键词： Sobolev space, Lipschitz-type space, embedding theorem, maximal function, space ofhomogeneous type.

THE MINIMAL PROPERTY OF THE CONDITION NUMBER OF INVERTIBLE LINEAR BOUNDED OPERATORS IN BANACH spaceS

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Numerical Mathematics A Journal of Chinese Universities(English Series) 2002年第1期11卷 63-69页

作者： Chen Guoliang(陈果良) Wei Musheng(魏木生) Department of Mathematics East China Normal University Shanghai 200062 Department of Mathematics East China Normal University Shanghai 200062

In this paper we show that in error estimates, the condition number κ(T) of any invertible linear bounded operator T in Banach spaces is minimal. We also extend the Hahn-Banach theorem and other related results.

关键词： Banach space, condition number, error estimate.