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Boundedness for commutators of fractional Hardy operators on Herz spaces

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Progress in Natural Science:Materials International 2007年第1期17卷 20-25页

作者： FU Zunwei, LIU Zongguang and lu Shanzhen ( School of Mathematical Sciences, beijing normal university, beijing 100875, china department of mathematics, Linyi normal university, Linyi 276005, china department of mathematics, china university of Mining and Technology, beijing 100083, china) School of Mathematical Sciences Beijing Normal University Beijing 100875 China department of mathematics Linyi Normal University Linyi 276005 China department of mathematics China University of Mining and Technology Beijing 100083 China

Some boundedness results are established for commutators generated by classical fractional Hardy operators and one-sided CMO functions on the homogeneous Herz spaces, which extends some known results.

关键词： fractional Hardy operator Hardy’s integral inequality commutator one-sided CMO function homogeneous Herz space.

A Remark on Multilinear Oscillatory Singular Integrals

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Acta Mathematica Sinica,English Series 2000年第4期16卷 655-668页

作者： Shanzhen lu Dunyan Yan department of mathematics, beijing normal university, beijing 100875. P. R. china department of mathematics Beijing Normal University Beijing 100875 P. R. China

In this paper we study multilinear oscillatory singular integrals with rough kernel and give a criterion of certain boundedness for this kind of operator

关键词： Multilinear oscillatory integrals Calderon-Zygmund kernel BLO space

Structure of 〔Na(DB18C6) (CH_3OH)〕_2W_6O_(19)·(DB18C6)·(CH_3OH)

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Chinese Journal of Structural Chemistry 1997年第3期16卷 172-176页

作者： lu Xiao-Ming CHU Yi-Ming DI Jing LIU Shun-Cheng(department of Chemistry, capital normal university beijing 100037, china) department of Chemistry Capital Normal University Beijing 100037 China

Complex [(DB18C6 ) (CH3OH )]2W6O19. (DB18C6 ) - (CH3OH),Mr=2630. 43, monoclinic, space group P21/c, a=18. 699 (5), b= 19. 568 (4), c=22. 785(5) A, β= 112. 91(2)°, V=7679(7) A, Z=4, D.=2- 275 g/cm3, F(000)= 4992, p= 92. 52 cm-1. The final R=0. 035 and Rw =0. 041 for 5689 observed reflections (I>3σ(I) ). The complex contains one hexatungstate anion and two sodiumcations. Each Na cation is inlaid in the cavity of one dibenzo-18-crown-6 (DB18C6)with six Na-O coordination bonds. In addition, it linked to O atom of CH3OH fromone side of DB18C6 and bonded to one of the terminal O atoms in hexatungstate anionfrom the other side. The two DB18C6 connected with hexatungstate symmetrically bythe long-distance interaction through the O- Na -O bonds with Na- O distances of2. 28(1)~2- 37(1 ) A W-O distances are 1. 68(2) ~2. 34(2) A. C-O distancesin methanol coordinated with cation are 1. 38 (4 ) ~ 1- 41 (4) A.

关键词： dibenzo-18-crown-6 (DB18C6) polyoxotungstate anion crystal structure

Pointwise estimates for the maximal multilinear singular integral operators

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Science china mathematics 2005年第12期48卷 1696-1706页

作者： HU Guo’en, LI Dengfeng & lu Shanzhen department of Applied mathematics, university of Information Engineering, P. O. Box 1001 -747, Zhengzhou 450002, china College of Mathematical and Information Sciences, Henan university, Kaifeng 475001, china department of mathematics, beijing normal university, beijing 100875, china department of Applied mathematics University of Information Engineering Zhengzhou 450002 China College of Mathematical and Information Sciences Henan University Kaifeng 475001 China department of mathematics Beijing Normal University Beijing 100875 China

Two pointwise estimates relating the maximal multilinear singular integral operators and some classical maximal operators are established. These pointwise estimates imply the rearrangement estimate and the BLO(Rn) est... 详细信息

关键词： multilinear singular integral,maximal operator,BMO (Rn),BLO (Rn).

On semisymmetric cubic graphs of order 6p^(2)

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Science china mathematics 2004年第1期47卷 1-17页

作者： lu Zaiping, WANG Changqun & XU MingyaoLMAM, School of Mathematical Sciences, Peking university, beijing 100871, china department of mathematics, Zhengzhou university, Zhengzhou 450052, chinaPresent address: department of mathematics, Qufu normal university, Qufu 273165, china. LMAM School of Mathematical Sciences Peking University Beijing China department of mathematics Zhengzhou University Zhengzhou China

A graph Γ is said to be G-semisymmetric if it is regular and there exists a subgroup G of A := Aut(Γ) acting transitively on its edge set but not on its vertex set. In the case of G = A, we call Γ a semisymmetric graph. The aim of this paper is to investigate (G-)semisymmetric graphs of prime degree. We give a group-theoretical construction of such graphs, and give a classification of semisymmetric cubic graphs of order 6p2 for an odd prime p.

关键词： (G-)semisymmetric graph, symmetric graph, bi-Cayley graph, regular covering, group action.

Dense coding scheme using superpositions of Bell-states and its NMR implementation

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Science china(Physics,Mechanics & Astronomy) 2005年第1期48卷 57-67页

作者： ZHANG Jingfu, XIE Jingyi, DENG Zhiwei & lu Zhiheng Key Laboratory for Quantum Information and Measurements, department of Physics, Tsinghua university, beijing 100084, china Center for Quantum Information, Tsinghua university, beijing 100084, china department of Materials Science and Engineering, beijing normal university, beijing 100875, china Testing and Analytical Center, beijing normal university, beijing 100875, china department of Physics, beijing normal university, beijing 100875, china Key Laboratory for Quantum Information and Measurements Department of Physics Tsinghua University Beijing 100084 China Center for Quantum Information Tsinghua University Beijing 100084 China department of Materials Science and Engineering Beijing 100875 China Testing and Analytical Center Beijing Normal University Beijing 100875 China department of Physics Beijing Normal University Beijing 100875 China

Dense coding using superpositions of Bell-states is proposed. The generalized Grover's algorithm is used to prepare the initial entangled states, and the reverse process of the quantum algorithm is used to determine the entangled state in the decoding measurement. Compared with the previous schemes, the superpositions of two Bell-states are exploited. Our scheme is demonstrated using a nuclear magnetic resonance (NMR)quantum computer. The corresponding manipulations are obtained. Experimental results show a good agreement between theory and experiment. We also generalize the scheme to transmit eight messages by introducing an additional two-state system.

关键词： dense coding, superpositions of Bell-states, generalized Grover's algorithm, nuclear magnetic res-onance, quantum computer.

Weighted weak type estimates for commutators of the Marcinkiewicz integrals

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Science china mathematics 2004年第1期47卷 83-95页

作者： DING Yong, lu Shanzhen & ZHANG Pudepartment of mathematics, beijing normal university, beijing 100875, china department of Information and Computing Science, Zhejiang Institute of Science and Technology, Hangzhou 310033, china department of mathematics Beijing Normal University Beijing China department of Information and Computing Science Zhejiang Institute of Science and Technology Hangzhou China

In this paper the authors give the weighted weak LlogL type estimates for a class of the higher order commutator generated by the Marcinkiewicz integral and a BMO function. In addition, the weak type norm inequalities... 详细信息

关键词： Marcinkiewicz integral, commutator, Ap weight, weak type estimate.

Weighted Boundedness for a Class of Rough Multilinear Operators

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Acta Mathematica Sinica,English Series 2001年第3期17卷 517-526页

作者： Yong DING Shan Zhen lu department of mathematics,beijing normal university,beijing 100875,P.R.china E-mail:dingy@*** lusz@*** department of mathematics Beijing Normal University Beijing 100875 P. R. China

In this paper we give the (L^p(ω~p),L^q(ω~q)) boundedness for a class of multilinear operators, which is similar to the higher-order commutator for the rough fractional *** our results the kernel function is merely ... 详细信息

关键词： Multilinear operator Fractional integral Rough kernel BMO A(p,q) weight

Estimates for eigenvalues of Laplacian operator with any order

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Science china mathematics 2007年第8期50卷 1078-1086页

作者： Fa-en WU~(1+) Lin-fen CAO~2 1 department of mathematics,beijing Jiaotong university,beijing 100044,china 2 department of mathematics,Henan normal university,Xinxiang 453007,china department of mathematics Beijing Jiaotong University Beijing China department of mathematics Henan Normal University Xinxiang China

Let D be a bounded domain in an n-dimensional Euclidean space ? n . Assume that $$0 < \lambda _1 \leqslant \lambda _2 \leqslant \cdots \leqslant \lambda _k \leqslant \cdots $$ are the eigenvalues of the Dirichlet Lapl... 详细信息

Let D be a bounded domain in an n-dimensional Euclidean space ? n . Assume that $$0 lues of the Dirichlet Laplacian operator with any order l: $$\left\{ \begin{gathered} ( - \vartriangle )^l u = \lambda u, in D \hfill \\ u = \frac{{\partial u}}{{\partial \vec n}} = \cdots = \frac{{\partial ^{l - 1} u}}{{\partial \vec n^{l - 1} }} = 0, on \partial D \hfill \\ \end{gathered} \right.$$ . Then we obtain an upper bound of the (k+1)-th eigenvalue λ k+1 in terms of the first k eigenvalues. $$\sum\limits_{i = 1}^k {(\lambda _{(k + 1)} - \lambda _i )} \leqslant \frac{1}{n}[4l(n + 2l - 2)]^{\tfrac{1}{2}} \left\{ {\sum\limits_{i = 1}^k {(\lambda _{(k + 1)} - \lambda _i )^{\tfrac{1}{2}} \lambda _i^{\tfrac{{l - 1}}{l}} \sum\limits_{i = 1}^k {(\lambda _{(k + 1)} - \lambda _i )^{\tfrac{1}{2}} \lambda _i^{\tfrac{1}{l}} } } } \right\}^{\tfrac{1}{2}} $$ . This ineguality is independent of the domain D. Furthermore, for any l ? 3 the above inequality is better than all the known results. Our rusults are the natural generalization of inequalities corresponding to the case l = 2 considered by Qing-Ming Cheng and Hong-Cang Yang. When l = 1, our inequalities imply a weaker form of Yang inequalities. We aslo reprove an implication claimed by Cheng and Yang.

关键词： Dirichlet problem eigenvalue estimate Laplacian operator 35P15 58G25