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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 {3. {4., 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) [a]school of mathematical sciences 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.

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, 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 7. Graduate {13. of the Chinese Academy of sciences, Beijing 10003., china 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 25 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.

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 {4. {3.,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 1. school of mathematical sciences 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

Theory of truth degrees of propositions in the logic system Ln^＊

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Science in china(Series F) 2006年第4期49卷 471-483页

作者： LI Jun1,2 & WANG Guojun1,3.1. Institute of Mathematics, Shaanxi normal University, Xi’an 710062, china 2. school of {3., Lanzhou University of Technology, Lanzhou 73.050, china 3. Research Center for Science, Xi’an Jiaotong University, Xi’an 71004., china 1. Institute of Mathematics Shaanxi Normal University Xi’an 710062 China 2. school of sciences Lanzhou University of Technology Lanzhou 730050 China 3. Research Center for Science Xi’an Jiaotong University Xi’an 710049 China

By means of infinite product of uniformly distributed probability spaces of cardinal n the concept of truth degrees of propositions in the n-valued generalized lu- kasiewicz propositional logic system Ln^＊ is introduced in the present paper. It is proved that the set consisting of truth degrees of all formulas is dense in [0,1], and a general expres- sion of truth degrees of formulas as well as a deduction rule of truth degrees is then obtained. Moreover, similarity degrees among formulas are proposed and a pseudo-metric is defined therefrom on the set of formulas, and hence a possible framework suitable for developing approximate reasoning theory in n-valued generalized lukasiewicz propositional logic is established.

关键词： truth degree similarity degree approximate reasoning.

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 -74., Zhengzhou 4.0002, china College of {3. and Information {4., Henan University, Kaifeng 4.5001, china Department of Mathematics, Beijing normal University, Beijing 100875, china 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).

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 {3.. P. R.{4. 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

A Spatiotemporal Analysis of Urban Growth:A Case Study for Jinan Municipality,china

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Chinese Journal of Population,Resources and Environment 2006年第4期4卷 48-53页

作者： Yu Bohua1,2,3.lu Changhe1,Zheng Xinqi 4.1.Institute of Geographical sciences and Natural Resources Research,Chinese Academy sciences,Beijing 100101,{3. 2.College of Resources Science&Technolgy,Beijing normal University,Beijing 100875,{3. 3.Graduate school of the Chinese Academy of Science(GUCAS),Beijing 10003.,{3. 4.Shandong normal University,Jinan,Shandong 250014.{3. Institute of Geographical sciences and Natural Resources Research Chinese Academy Sciences Beijing 100101 China College of Resources Science & Technolgy Beijing Normal University Beijing 100875 China Graduate school of the Chinese Academy of Science(GUCAS) Beijing 100039China Institute of Geographical Sciences and Natural Resources Research Chinese Academy Sciences Beijing 100101 China Shandong Normal University Jinan Shandong 250014 China

china is experiencing a process of rapid industrialization and urbanization at the cost of agricultural land and environment, particularly in the costal *** study takes Jinan as a case presenting a time-series analysis of urban land expansion from 3.3.to *** results show that the urban expansion of Jinan city mainly took place in the last 100 years,especially after the economic reform in *** development and economic growth, urban population growth and migration policies were factors driving the urban land *** sprawl resulted in a disappearance of wetlands and a great loss of agricultural land,and over-pumping of ground water that led to disappearance of the city's feature, namely"the city of springs".

关键词： urban land expansion driving forces environmental effects Jinan

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 {3.,{4. Department of Information and Computing Science, Zhejiang Institute of Science and Technology, Hangzhou 3.003.,{4. 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.

Strongly Singular Convo1ution Operators on the Weighted Herz-Type Hardy Spaces

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Acta Mathematica Sinica,English Series 1998年第1期14卷 67-76页

作者： Li Xiaochun lu shanzhen Department of Mathematics, Beijing normal University, Beijing {3.,{4.

Let 01, w2 ∈A1 （Muckenhoupt-class）. In this paper the authors prove that the strongly singular convolution operators are bounded from the homogeneous weighted Herz-type Hardy spaces HKqα,p（w1; w2） to the homogeneous weighted Herz spaces Kqα,p（w1;w2）, provided α=n（1--1/q）. Moreover, the boundedness of these operators on the non-homogeneous weighted Herz-type Hardy spaces HKqα,p（w1, w2） is also investigated.

关键词： Strongly singular convolution operator Hardy space