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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) [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.

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

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 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).

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 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 100875, china

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

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 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 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

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 (beijing normal 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

A MACRO-SCALE SEMI-DISTRIBUTED HYDROLOGICAL MODEL AND APPLICATION TO THE DATONG RIVER VALLEY

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Journal of Hydrodynamics 2005年第6期17卷 667-676页

作者： YANG Zhi-feng LIU lu-liu SHEN Zhen-yao GORDON G. Huang State Key Laboratory of Water Environmental Simulation School of Environment Beijing Normal Uni- versity Beijing 100875 China National Climate Center Beijing 100081 China Faculty of Engineering University of Regina Canada

A daily distributed hydrological model was developed using routine hydro meteorological data on the basis of the raster DEM and land cover data. Then the model was used to model daily runoff of the Datong River Valley located in the upper catchment of the Yellow River Basin. The runoff comprises surface flow, subsurface flow and ground water flow. Evapotranspiration comprises canopy evaporation, snow sublimation and soil evapotranspiration. The infiltration to the soil was estimated with improved Green-Ampt model, and the potential evapotranspiration is estimated with Morton CRAE method, which only needs the routine meteorological data. Simulation results and the comparison with semi distributed SluRP hydrological model show that the structure of the model presented herein is reasonable.

关键词： hydrological model Yellow River GIS runoff

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. 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.