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| 1 | L^p-Boundedness of Marcinkiewicz Integrals with Hardy Space Function Kernels | Yong Ding Department of Mathematics, Beijing Normal University, Beijing 100875, P. R. China Dashan Fan Department of Mathematics, Anhui University and University of Wisconsin-Milwaukee. MW 53201 USA Yibiao Pan Department of Mathematics, University of Pittsburgh. Pittsburgh. Pennsylvania 15260. USA | 2000 | Acta Mathematica Sinica,English Series2000，16，4： | 88 |
| 2 | Hausdorff Operators on Function Spaces显示文摘The authors mainly study the Hausdorff operators on Euclidean space R^n. They establish boundedness of the Hausdorff operators in various function spaces, such as Lebesgue spaces, Hardy spaces, local Hardy spaces and Herz type spaces. The results reveal that the Hausdorff operators have better performance on the Herz type Hardy spaces H Kα,pq (R^n) than their performance on the Hardy spaces H^p(R^n) when 0 < p < 1. Also, the authors obtain some new results and reprove or generalize some known results for the high dimensional Hardy operator and adjoint Hardy operator. | Jiecheng CHEN Dashan FAN Jun LI | 2012 | Chinese Annals of Mathematics,Series B2012，33，4： | 23 |
| 3 | Certain oscillatory integrals on unit square and their applications显示文摘Let Q2 = [0, 1]2 be the unit square in two dimension Euclidean space R2. We study the Lp boundedness properties of the oscillatory integral operators Tα,β defined on the set S(R3) of Schwartz test functions f by Tα,βf(x,y,z) = Q2 f(x - t,y - s,z - tksj)e-it-β1s-β2t-1-α1s-1-α2dtds, where β1 > α1 0, β2 > α2 0 and (k, j) ∈ R2. As applications, we obtain some Lp boundedness results of rough singular integral operators on the product spaces. | FAN DaShan WU HuoXiong | 2008 | Science China Mathematics2008，51，10： | 6 |
| 4 | Boundedness of Hausdorff operators on Lebesgue spaces and Hardy spaces显示文摘In this paper, we study the boundedness of the Hausdorff operator H_? on the real line R. First, we start with an easy case by establishing the boundedness of the Hausdorff operator on the Lebesgue space L^p(R)and the Hardy space H^1(R). The key idea is to reformulate H_? as a Calder′on-Zygmund convolution operator,from which its boundedness is proved by verifying the Hrmander condition of the convolution kernel. Secondly,to prove the boundedness on the Hardy space H^p(R) with 0 < p < 1, we rewrite the Hausdorff operator as a singular integral operator with the non-convolution kernel. This novel reformulation, in combination with the Taibleson-Weiss molecular characterization of H^p(R) spaces, enables us to obtain the desired results. Those results significantly extend the known boundedness of the Hausdorff operator on H^1(R). | Jiecheng Chen Jiawei Dai Dashan Fan Xiangrong Zhu | 2018 | Science China Mathematics2018，61，9： | 5 |
| 5 | Littlewood-Paley operators with variable kernels显示文摘In this paper we study a certain directional Hilbert transform and the boundedness on some mixed norm spaces. As one of applications, we prove the Lp-boundedness of the Littlewood-Paley operators with variable kernels. Our results are extensions of some known theorems. | CHEN Jiecheng, DING Yong & FAN Dashan Department of Mathematics, Zhejiang University (Xixi Campus), Hangzhou 310028, China School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China Department of Mathematics, University of Wisconsin-Milwaukee, Milwaukee WI 53201, USA Department of Mathematics, Central China Normal University, Wuhan 430074, China | 2006 | Science China Mathematics2006，49，5： | 4 |
| 6 | Estimates for wave and Klein-Gordon equations on modulation spaces显示文摘We prove that the fundamental semi-group eit(m 2I+|Δ|)1/2(m = 0) of the Klein-Gordon equation is bounded on the modulation space M ps,q(Rn) for all 0 < p,q ∞ and s ∈ R.Similarly,we prove that the wave semi-group eit|Δ|1/2 is bounded on the Hardy type modulation spaces μsp,q(Rn) for all 0 < p,q ∞,and s ∈ R.All the bounds have an asymptotic factor tn|1/p 1/2| as t goes to the infinity.These results extend some known results for the case of p 1.Also,some applications for the Cauchy problems related to the semi-group eit(m2I+|Δ|)1/2 are obtained.Finally we discuss the optimum of the factor tn|1/p 1/2| and raise some unsolved problems. | CHEN JieCheng FAN DaShan | 2012 | Science China Mathematics2012，55，10： | 4 |
| 7 | Sharpness of some properties of weighted modulation spaces显示文摘We obtain some optimal properties on weighted modulation spaces. We find the necessary and sufficient conditions for product inequalities, convolution inequalities and embedding on weighted modulation spaces. Especially, we establish the analogue of the sharp Sobolev embedding theorem on weighted modulation spaces. | GUO WeiChao FAN DaShan WU HuoXiong ZHAO GuoPing | 2016 | Science China Mathematics2016，59，1： | 3 |
| 8 | THE WEIGHTED HERZ-TYPE HARDY SPACES hK_q^(α,p)(ω_1,ω_2)显示文摘Let (.the Muckenhoupt class). In this paper, the author introduce the weighted Herz-type Hardy spaces (w2) and present their atomic decomposition. Using the atomic decomposition, the author find out their dual spaces, establish the boundedness on these spaces of the pseudo-differential operators of order zero and show that , the class of C(Rn)-functions with compactly support, is dense in and there is a subsequence, which converges in distrbutional sense to some distribution of , of any bounded sequence in In addition, the author also set up the boundedness of some non-linear quantities in compensated compactness. | Fan Dashan and Yang Dachun (University of WI~Milwaukee, U. S. A. and Beijing Normal University, China) | 1997 | Analysis in Theory and Applications1997，13，4： | 2 |
| 9 | A Discrete Singular Integral Operator(In Memory of Professor Long Ruilin) | Fan Dashan (Department of Mathematical Sciences,University of Wisconsin-Milwaukee,Milwaukee,WI 53201,USA)(Email:fan@alpha1.csd.uwm.edu)Lu Shanzhen (Department of Mathematics,Beijing Normal University,Beijing 100875,China)(Email:lusz@sun.ihep.ac.cn)Pan Yibiao (Department of Mathematics and Statistics,University of Pittsburgh,Pittsburgh,PA 15260,USA)(Email:yibiao@tomato.math.pitt.edu) | 1998 | Acta Mathematica Sinica,English Series1998，14，2： | 1 |
| 10 | A note on a rough singular integral operator 显示文摘 | Guo Kanghui and Pan Yibiao | | preprint0，，： | 1 |
| 11 | Regularity in Morrey Spaces of Strong Solutions to Nondivergence Elliptic Equations with VMO Coefficients显示文摘 | Dashan Fan Shanzhen Lu Dachun Yang | 1998 | Georgian Mathematical Journal1998，，5： | 1 |
| 12 | An Oscillating Operator Related to Wave Equations in the Block Spaces显示文摘在这篇文章,我们在欧几里德几何学的空间并且在花托上为波浪方程学习与 Cauchy 问题有关的某些震荡的 multipliers。我们获得在结束点,这些操作员从 L p 空格被围住到某些块空格。 | Dashan FAN Lijing SUN | 2011 | Acta Mathematica Sinica,English Series2011，27，1： | 1 |
| 13 | Hardy spaces on compact Lie groups显示文摘 | Blank B E Fan Dashan | | 0，，3： | 1 |
| 14 | A singular integral operator with rough kernel显示文摘 | Fan Dashan Pan Yibiao | | 0，，12： | 1 |
| 15 | Singular integral operators with rough kernels supported by subvarieties显示文摘 | Fan Dashan Pan Yibiao | | 0，，4： | 1 |
| 16 | L:'-boundedness of Marcinkiewicz integrals with Hardy space function kernel 显示文摘 | DING Yong FAN Dashan PAN Yibiao | 2002 | Acta Math Sinica: English Series2002，16，： | 1 |
| 17 | Certain operators with rough singular kernels显示文摘 | Chen Jiechen Fan Dashan Ying Yiming | | 0，，3： | 1 |
| 18 | A note on a Marcinkiewicz integral operator显示文摘 | CHEN Jiecheng FAN Dashan PAN Yibiao | 2001 | Math Nachr2001，227，： | 1 |
| 19 | Certain operators with rough singular kernels显示文摘 | Chen Jiecheng Fan Dashan Ying Yiming | 2003 | Canad J Math2003，55，3： | 1 |
| 20 | Singular integral operators on function spaces显示文摘 | Chen Jiecheng Fan Dashan Ying Yiming | 2002 | Joun Math Anal Appl2002，276，： | 1 |
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