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| 1 | THE CENTRAL BMO SPACES AND LITTLEWOOD-PALEY OPERATORS显示文摘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 classes of general Littlewood-Paley operators. | Lu Shanzhen and Yang Dachun (Beijing Normal University, China) | 1995 | Analysis in Theory and Applications1995，11，3： | 49 |
| 2 | Weighted weak type estimates for commutators of the Marcinkiewicz integrals显示文摘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 for the Marcinkiewicz integral and its commutators with different weight functions are also discussed. | 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 | 2004 | Science China Mathematics2004，47，1： | 25 |
| 3 | Endpoint estimates for n-dimensional Hardy operators and their commutators显示文摘In this paper,the sharp bound for the weak-type(1,1) inequality for the n-dimensional Hardy operator is obtained.Moreover,the precise norms of generalized Hardy operators on the type of Campanato spaces are worked out.As applications,the corresponding norms of the Riemann-Liouville integral operator and the n-dimensional Hardy operator are deduced.It is also proved that the n-dimensional Hardy operator maps from the Hardy space into the Lebesgue space.The endpoint estimate for the commutator generated by the Hardy operator and the(central) BMO function is also discussed. | ZHAO FaYou FU ZunWei LU ShanZhen | 2012 | Science China Mathematics2012，55，10： | 19 |
| 4 | Explicit constants for Hardy’s inequality with power weight on n-dimensional product spaces显示文摘In this paper, Hardy operator H on n-dimensional product spaces G = (0, ∞)n and its adjoint operator H* are investigated. We use novel methods to obtain two main results. One is that we characterize the sufficient and necessary conditions for the operators H and H* being bounded from Lp(G, xα) to Lq(G, xβ), and the bounds of the operators H and H* are explicitly worked out. The other is that when 1 < p = q < +∞, norms of the operators H and H* are obtained. | WANG ShiMo LU ShanZhen YAN DunYan | 2012 | Science China Mathematics2012，55，12： | 12 |
| 5 | Some Characterizations of Weighted Herz-type Hardy Spaces and Their Applications | Lu Shanzhen (Department of Mathematics,Beijing Normal University,Beijing,100875,China)(E-mail:lusz@bnu.edu.cn)Yang Dachun (Department of Mathematics,Beijing Normal University,Beijin9,100875,China)(E-mail:dcyang@bnu.edu.cn) | 1997 | Acta Mathematica Sinica,English Series1997，13，1： | 10 |
| 6 | ON A MULTILINEAR OSCILLATORY SINGULAR INTEGRAL OPERATOR(I)显示文摘ONAMULTILINEAROSCILLATORYSINGULARINTEGRALOPERATOR(I)CHENWENGUHUGUOENLUSHANZHENManuscriptreceivedOctober18,1994.RevisedDece... | CHEN WENGU * HU GUOEN * LU SHANZHEN * Manuscript received October 18, 1994. Revised December 13, 1995. *Department of Mathematics, Beijing Normal University, Beijing 100875, China. **Project supported by the National Natural Scienc | 1997 | Chinese Annals of Mathematics,Series B1997，18，2： | 8 |
| 7 | Toeplitz operators related to strongly singular Calderón-Zygmund operators显示文摘In this paper, the boundedness of Toeplitz operator Tb(f) related to strongly singular Calderón-Zygmund operators and Lipschitz function b ∈(Λ)β0(Rn) is discussed from Lp(Rn) to Lq(Rn),1/q=1/p-β0/n, and from Lp(Rn) to Triebel-Lizorkin space (F)β0,∞p. We also obtain the boundedness of generalized Toeplitz operator Θbα0 from Lp(Rn) to Lq(Rn), 1/q=1/p-α0+β0/n.All the above results include the corresponding boundedness of commutators. Moreover, the boundedness of Toeplitz operator Tb(f) related to strongly singular Calderón-Zygmund operators and BMO function b is discussed on Lp(Rn), 1 < p < ∞ . | LIN Yan LU Shanzhen | 2006 | Science China Mathematics2006，49，8： | 8 |
| 8 | Commutators of n-dimensional rough Hardy operators显示文摘In this paper, we study central BMO estimates for commutators of n-dimensional rough Hardy operators. Furthermore, λ-central BMO estimates for commutators on central Morrey spaces are discussed. | FU ZunWei LU ShanZhen ZHAO FaYou | 2011 | Science China Mathematics2011，54，1： | 7 |
| 9 | GLOBAL REGULARITY IN HOMOGENEOUS MORREY-HERZ SPACES OF SOLUTIONS TO NONDIVERGENCE ELLIPTIC EQUATIONS WITH VMO COEFFICIENTS显示文摘 | Lu Shanzhen Tao Shuangping | 2007 | Journal of Partial Differential Equations2007，20，2： | 6 |
| 10 | INHOMOGENEOUS BESOV AND TRIEBEL-LIZORKING SPACES ON SPACES OF HOMOGENEOUS TYPE显示文摘The authors introduce the inhomogeneous esov space and the inhomogeneous Triebel-Lizorkin space on spaces of homogeneous type; and present their atom and molecule decompositions, their dual spaces and the complex interpolation theorems. They also establishe the relation between the homogoeneous Besov space and the inhomogeneous one, and between the homogeneous Triebel-Lizorkin space and the inhomogeneous one. Moreover,they establish T1 theorems for these inhomogeneous spaces when a≠0, and applythese T1 theorems to give new characterizations of these | Yongsheng Han (1) Shanzhen Lu (2) Dachun Yang (2) | 1999 | Analysis in Theory and Applications1999，15，3： | 6 |
| 11 | Boundedness for commutators of fractional Hardy operators on Herz spaces显示文摘一些围住的海角结果为古典部分强壮的操作符和片面 CMO 函数在同类的 Herz 空格产生的整流器被建立,它扩大一些已知的结果。 | FU Zunwei LIU Zongguang LU Shanzhen | 2007 | Progress in Natural Science:Materials International2007，17，1： | 5 |
| 12 | A characterization of λ-central BMO space显示文摘我们经由 n 维的强壮的操作员的整流器的固定给中央 BMO 空间的描述。 | Fayou ZHAO Shanzhen LU | 2013 | Frontiers of Mathematics in China2013，8，1： | 3 |
| 13 | MULTILINEAR CALDERóN-ZYGMUND OPERATOR ON MORREY TYPE SPACES——In Memory of Professor Yongsheng Sun显示文摘In this paper, the authors study the boundedness of a class of multi-sublinear operators on the product of Morrey, Herz-Morrey and generalized Morrey spaces, respectively. As their special cases, the corresponding results of multilinear Calderon-Zygmund operator can be obtained. | Yan Lin Shanzhen Lu | 2006 | Analysis in Theory and Applications2006，22，4： | 3 |
| 14 | Strongly Singular Convo1ution Operators on the Weighted Herz-Type Hardy Spaces | Li Xiaochun Lu Shanzhen Department of Mathematics, Beijing Normal University, Beijing 100875, China | 1998 | Acta Mathematica Sinica,English Series1998，14，1： | 3 |
| 15 | Multipliers and Herz type spaces显示文摘Hrmander condition for boundedness of multiplier operators will be replaced by a weaker condition described by certain weighted or non-weighted Herz spaces. Some results on boundedness of multiplier operators are then established. As direct corollaries of main theorems in this paper, several celebrated results on boundedness of multiplier operators will be improved or deduced. | LU ShanZhen School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China | 2008 | Science China Mathematics2008，51，10： | 2 |
| 16 | Multiple weighted estimates for maximal vector-valued commutator of multilinear Calderon-Zygmund singular integrals显示文摘这份报纸为最大的珍视向量的 multilinear 与多重加权的标准不平等担心单个操作员和最大的整流器。最大的珍视向量的 multilinear 的 Cotlar 类型不平等单个积分操作员被获得。在另一方面,为单个积分和最大的珍视向量的整流器也是的二种最大的珍视向量的 multilinear 的锋利的最大的功能的 pointwise 估计建立了。由新变体的一个类的加权的估计,最大的操作员, Cotlars 不平等和锋利的最大的函数估计,为为 multilinear 的最大的珍视向量的整流器的 multilinear 操作符和那些的最大的珍视向量的单个积分的多重加权的强壮的估计和弱估计单个积分被获得。 | Dongxiang CHEN Shanzhen LU Suzhen MAO | 2017 | Frontiers of Mathematics in China2017，12，3： | 2 |
| 17 | Boundedness for a class of fractional integrals with a rough kernel related to block spaces显示文摘我们在 Triebel-Lizorkin 空格用一个不平的核证明部分积分的固定,在不平的核属于块空间的地方并且不需要任何时刻在联合起来的范围上满足条件。 | Xiao YU Shanzhen LU | 2016 | Frontiers of Mathematics in China2016，11，1： | 2 |
| 18 | CALDER6N-ZYGMUND OPERAORS ON THE HARDY SPACES OF WEIGHTED HERZ TYPE显示文摘Applying the decomposition theorems in [1] and [2] , we obtain the boundedness theorem of Calderbn-Zygmund operator of type 6 on the Hardy spaces of weighted Herz type and establish interpolation theorem of linear operators on the weighted Herz spaces. - | Liu Weiquan and Lu Shanzhen(Beijing Normal University, China) | 1997 | Analysis in Theory and Applications1997，13，2： | 2 |
| 19 | The continucity of commutators on Herz-type spaces显示文摘 | Lu Shanzhen Yang Dachun | 1997 | Michigan Math J1997，44，： | 2 |
| 20 | On Marcinkiewicz integral with rough kernels显示文摘 | Lu Shanzhen | 2008 | Frontiers of Math in China2008，3，： | 1 |
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