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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 ( {2. of {2. sciences, beijing normal university, beijing 100875, china Department of Mathematics, Linyi normal university, Linyi 2.6005, china Department of Mathematics, china university of Mining and Technology, beijing 100083, china) [a]school of mathematical {2. Beijing Normal University Beijing China [b]Departhent of Mathematics Linyi Normal University Linyi China [c]Departhent of Mathematics China University of Mining and Technology Beijing 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.

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, {2. of Information Engineering, P. O. Box 1001 -747, Zhengzhou 450002.{2. College of mathematical and Information sciences, Henan {2., Kaifeng 475001,{2. Department of Mathematics, beijing normal university, beijing 100875,{2. 1. Department of Applied Mathematics University of Information Engineering P.O.Box 1001-747 450002 Zhengzhou China 2. College of mathematical and Information sciences Henan University 475001 Kaifeng China 3. Department of Mathematics Beijing Normal University 100875 Beijing 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).

Characterization for commutators of n-dimensional fractional Hardy operators

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Science china Mathematics 2007年第10期50卷 1418-1426页

作者： Zun-wei FU~(1,2. Zong-guang LIU~3 Shan-zhen lu~(1+) Hong-bin WANG~3 ~1 school of {2. {2.,beijing normal university,beijing 100875,china ~2.Department of Mathematics,Linyi normal university,Linyi 2.6005,china ~3 Department of Mathematics,china university of Mining and Technology (beijing),beijing 100083,china 1. school of mathematical {2. Beijing Normal University Beijing 100875 China 2. Department of Mathematics Linyi Normal University Linyi 276005 China 3. Department of Mathematics China University of Mining and Technology (Beijing) Beijing 100083 China

In this paper,it was proved that the commutator H_(β,b)generated by an n-dimensional fractional Hardy operator and a locally integrable function b is bounded from L^(p1)(R^n)to L^(p2.(R^n)if and only if b is a CMO(R^... 详细信息

关键词： n-dimensional fractional Hardy operator, commutator, C(M)O function, homogeneous Herz space

THE CENTRAL BMO SPACES AND LITTLEWOOD-PALEY OPERATORS

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Analysis in Theory and Applications 1995年第3期11卷 72-94页

作者： lu shanzhen and Yang Dachun ({2. {2. university, china) 1. Department of Mathematics Beijing Normal University 100875 Beijing PRC

The authors give a characterization of central bounded mean oscillation space CBMO2.Rγ) in terms of the central Carleson measure. Using this character, the authors establish the CBMO2.Rγ)-boundedness for several cla... 详细信息

关键词： BMO II THE CENTRAL BMO SPACES AND LITTLEWOOD-PALEY OPERATORS

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 {2. {2., Peking university, beijing 100871, china Department of Mathematics, Zhengzhou university, Zhengzhou 450052. chinaPresent address: Department of Mathematics, Qufu normal university, Qufu 2.3165, china. 1. LMAM School of Mathematical Sciences Peking University 100871 Beijing China 3. Department of Mathematics Zhengzhou University 450052 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.

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,{2., {2. 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

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,{2., {2. 100875, china Department of Information and Computing Science, Zhejiang Institute of Science and Technology, Hangzhou 310033, china 1. Department of Mathematics Beijing Normal University 100875 Beijing China 2. Department of Information and Computing Science Zhejiang Institute of Science and Technology 310033 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.

Origin of the Red Earth sequence on the northeastern Tibetan Plateau and its implications for regional aridity since the middle Miocene

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Science china Earth sciences 2006年第5期49卷 505-517页

作者： WANG Xianyan1,7, lu Huayu1,2. JI Junfeg3, WANG Xiaoyong1,7, ZHAO Jingbo4, HUANG Baochun5 & LI Zhen6 1. SKLLQG, Institute of Earth Environment, Chinese Academy of sciences, Xi’an 710075,{2. 2. Department of Urban and Resources sciences, Nanjing university, Nanjing 2.0093,{2. 3. Department of Earth sciences, Nanjing university, Nanjing 2.0093,{2. 4. Department of Geography, Shaanxi normal university, Xi’an 710062.{2. 5. Institute of Geology and Geophysics, Chinese Academy of sciences, beijing 10002.,{2. 6 Department of Geography, Qinghai normal university, Xining 810008,{2. 7. Graduate school of the Chinese Academy of sciences, beijing 100039,{2. 1. SKLLQG Institute of Earth Environment Chinese Academy of Sciences Xi’an 710075 China 7. Graduate school of the Chinese Academy of sciences Beijing 100039 China 2. Department of Urban and Resources sciences Nanjing University Nanjing 210093 China 3. Department of Earth sciences Nanjing University Nanjing 210093 China 4. Department of Geography Shaanxi Normal University Xi’an 710062 China 5. Institute of Geology and Geophysics Chinese Academy of Sciences Beijing 100029 China 6. Department of Geography Qinghai Normal University Xining 810008 China

The Red Earth deposit around Xining, northeastern Tibetan Plateau, has beenstudied in terms of soil micro-structure, grain-size distribution, major- and trace-elementchemistry and magne-tostratigraphy. Field investigations indicate that the Red Earth sequenceconsists of 2. visually definable yellow-brown and weakly-developed soils interbedded with reddishstrongly-developed soils, and has a similar structure to the aeolian Red Clay deposit on the ChineseLoess Plateau. Grain-size analysis shows that the Red Earth deposit is very fine-grained with anegligible sand fraction ( > 63 μm). Thin-section observations under light microscopy show that thedeposit has a clayey texture and the coarse fraction ( > 10 μm) mainly consists of quartz,feldspar and micas. Pyroxene and hornblende were also observed. This mineralogical composition ofthe coarse fraction is similar to that of the Quaternary loess. In addition, all of the mineralgrains are semi angular semi-angular and are generally finer than 63 μm. There is a good agreementbetween the major and minor trace element chemistry of loess-soil units and the Red Earth *** REE distributions of the loess-soil and the Red Earth deposit are similar in shape, withenriched LREE and fairly flat HREE profiles and a clear negative Eu anomaly. The geochemicalcharacteristics of the Red Earth deposit are also identical to those of upper continental crust,thus indicating a wind-blown origin. Magnetostratigraphic investigation shows that onset of the RedEarth deposition predates 11.4 Ma BP (13.6 Ma at a nearby site). The distribution of the reportedMiocene aeolian loess at Qin''an of the Loess Plateau is still unknown. Our results indicate thatthis aeolian deposit had extended to the northeastern Tibetan Plateau by at least the middleMiocene. The similarity of the element geochemistry between the Red Earth deposit and the overlyingloess shows that they may have similar sources and dynamic transport system, and may indicate thatthe

关键词： Red Earth deposit, Northeastern Tibetan Plateau, aeolian deposit, aridity of Asia, the middle Miocene.

Electrochemical studies of nickel deposition from aqueous solution in super-gravity field

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Science china(Technological sciences) 2007年第1期50卷 39-50页

作者： GUO ZhanCheng1,2. GONG YingPeng2.& lu WeiChang2.1 Metallurgical & Ecological {2., university of Science and Technology, {2. 100083, china 2.Institute of Process Engineering, Chinese Academy of sciences, {2. 100080, china 1. Metallurgical & Ecological school University of Science and Technology Beijing 100083 China 2. Institute of Process Engineering Chinese Academy of Sciences Beijing 100080 China

The effect of super-gravity on electrochemical deposition of nickel from aqueous solution was studied. The SEM pictures show that the microstructure of nickel film deposited under the super-gravity condition is finer and more uniform compared with that obtained in normal gravity condition, and the crystal grains diminish with the increase of super-gravity coefficient. The XRD patterns indicate that the arrangement of crystalline grains of nickel film deposited under the super-gravity field is more regular, and the crystalline grain sizes decrease with the increase of super-gravity coefficient. Toughness, tensile stress and hardness of the nickel film are markedly raised with the increase of super-gravity coefficient, and hydrogen content in the nickel film decreases with the increase of super-gravity coefficient. From the polarization curves of hydrogen evolution reaction under the super-gravity condition, a significant reduction of over-potential on electrode was found when current density increased. The process of hydrogen evolution reaction was enhanced under the super-gravity condition. The electro-deposition rate, the microstructure and properties of deposited nickel film under super-gravity condition were still affected by the relative orientation between inertia force and depositing surface. It is favorable to gain the nickel film with better mechanic properties when inertia force orientates vertically towards depositing surface. Keywords super-gravity - electrochemistry - electro-deposition - nickel film Supported by the Notional Natural Science Foundation of china (Grant No. 50674011)

关键词： super-gravity electrochemistry electro-deposition nickel film