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Boundedness of an Oscillating Multiplier on Triebel-Lizorkin Spaces

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Acta Mathematica Sinica,English Series 2010年第11期26卷 2071-2084页

作者： Wei CAO Jie Cheng CHEN da shan fan Department of Mathematics Zhejiang University Hangzhou 310027 P. R. China Department of Mathematics University of Wisconsin-Milwaukee Milwaukee WI53217 USA

Abstract In this paper, we study Triebel-Lizorkin space estimates for an oscillating multiplier mΩ,α,β. This operator was initially studied by Wainger and by Fefferman-Stein in the Lebesgue spaces. We obtain the bo... 详细信息

关键词： Oscillating multiplier Triebel-Lizorkin spaces atomic decomposition

L^p Bounds for Singular Integrals with Rough Kernels on Product Domains

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Acta Mathematica Sinica,English Series 2012年第1期28卷 133-144页

作者： Li MA da shan fan Huo Xiong WU School of Mathematics and Computer Sciences Gannan Normal UniversityGanzhou 341000P.R.China Department of Mathematics University of Wisconsin-MilwaukeeMilwaukeeWI 53201USA School of Mathematical Sciences Xiamen UniversityXiamen 361005P.R.China

This paper is concerned with singular integral operators on product domains with rough kernels both along radial direction and on spherical surface. Some rather weaker size conditions, which imply the L^P-boundedness ... 详细信息

关键词： Singular integral rough kernel product domain Littlewood-Paley theory Fourier transform estimate

Approximation of the Fractional Schrodinger Propagator on Compact Manifolds

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Acta Mathematica Sinica,English Series 2021年第10期37卷 1485-1496页

作者： Jie Cheng CHEN da shan fan Fa You ZHAO Department of Mathematics Zhejiang Normal UniversityJinhua 321000P.R.China Department of Mathematical Sciences University of Wisconsin–MilwaukeeMilwaukeeWI 53201USA Department of Mathematics Shanghai UniversityShanghai 200444P.R.China

Let L be a second order positive,elliptic differential operator that is self-adjoint with respect to some C^(∞)density dx on a compact connected manifold *** proved that if 00.

关键词： Schrodinger propagator almost everywhere convergence compact manifolds

Multilinear Hausdorff Operators and Their Best Constants

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Acta Mathematica Sinica,English Series 2012年第8期28卷 1521-1530页

作者： Jie Cheng CHEN da shan fan Chun Jie ZHANG Department of Mathematics Zhejiang Normal University Department of Mathematics Zhejiang University Department of Mathematics University of Wisconsin-MilwaukeeMilwaukeeWI53201USA School of Science Hangzhou Dianzi University

In this paper, we study two different extensions of the Hausdorff operator to the multilinear case. Boundedness on Lebesgue spaces and Herz spaces is obtained. The bound on the Lebesgue space is optimal. Our results a... 详细信息

关键词： Hausdorff operator multilinear Herz space sharp bounds

The burden of upper motor neuron involvement is correlated with the bilateral limb involvement interval in patients with amyotrophic lateral sclerosis:a retrospective observational study

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Neural Regeneration Research 2025年第5期20卷 1505-1512页

作者： Jieying Wu shan Ye Xiangyi Liu Yingsheng Xu Dongsheng fan Department of Neurology Peking University Third HospitalBeijingChina Beijing Municipal Key Laboratory of Biomarker and Translational Research in Neurodegenerative Diseases BeijingChina Key Laboratory for Neuroscience National Health Commission/Ministry of EducationPeking UniversityBeijingChina

Amyotrophic lateral sclerosis is a rare neurodegenerative disease characterized by the involvement of both upper and lower motor *** bilateral limb involvement significantly affects patients'daily lives and may lead them to be confined to ***,the effect of upper and lower motor neuron impairment and other risk factors on bilateral limb involvement is *** address this issue,we retrospectively collected data from 586 amyotrophic lateral sclerosis patients with limb onset diagnosed at Peking University Third Hospital between January 2020 and May 2022.A univariate analysis revealed no significant differences in the time intervals of spread in different directions between individuals with upper motor neuron-dominant amyotrophic lateral sclerosis and those with classic amyotrophic lateral *** used causal directed acyclic graphs for risk factor determination and Cox proportional hazards models to investigate the association between the duration of bilateral limb involvement and clinical baseline characteristics in amyotrophic lateral sclerosis *** factor analyses revealed that higher upper motor neuron scores(hazard ratio[HR]=1.05,95%confidence interval[CI]=1.01–1.09,P=0.018),onset in the left limb(HR=0.72,95%CI=0.58–0.89,P=0.002),and a horizontal pattern of progression(HR=0.46,95%CI=0.37–0.58,P<0.001)were risk factors for a shorter interval until bilateral limb *** results demonstrated that a greater degree of upper motor neuron involvement might cause contralateral limb involvement to progress more quickly in limb-onset amyotrophic lateral sclerosis *** findings may improve the management of amyotrophic lateral sclerosis patients with limb onset and the prediction of patient prognosis.

关键词： amyotrophic lateral sclerosis bilateral limb involvement Cox proportional hazards regression model horizontal spread restricted cubic spline analysis time interval upper motor neuron vertical spread

Oscillatory hyper Hilbert transforms along curves

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Applied Mathematics(A Journal of Chinese Universities) 2009年第3期24卷 336-342页

作者： CHEN Jie-cheng fan da-shan WANG Meng Dept. of Math. Zhejiang University Hangzhou 310027 China Dept. of Mathematical Sciences University of Wisconsin-Milwaukee Milwaukee Wisconsin 53201

The hyper Hilbert transform Tnf（x） =∫-1^1 f（x - Γ（t））e^-i｜t｜-β｜t｜^-1-αdt along an appropriate curve Γ（t） on R^n is investigated,where β 〉 α 〉 *** L^p boundedness theorem of T4 is obtained,which is... 详细信息

关键词： hyper Hilbert transform curve

Boundedness of Hausdorff operators on some product Hardy type spaces

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Applied Mathematics(A Journal of Chinese Universities) 2012年第1期27卷 114-126页

作者： CHEN Jie-cheng fan da-shan ZHANG Chun-jie Department of Mathematics Zhejiang Normal UniversityJinhua 321004China Department of Mathematics University of WisconsimMilwaukeeMilwaukeeWI 53201USA School of Science Hangzhou Dianzi UniversityHangzhou 310018China

We study Hausdorff operators on the product Besov space B0,1 1 （Rn ×Rm） and on the local product Hardy space h1 （Rn ×Rm）. We establish some boundedness criteria for Hausdorff operators on these function spaces.

关键词： Hausdorff operator atomic decomposition product Besov space product Hardy space productlocal Hardy space.

Hausdorf operators on Euclidean spaces

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Applied Mathematics(A Journal of Chinese Universities) 2013年第4期28卷 548-564页

作者： CHEN Jie-cheng fan da-shan WANG Si-lei Department of Mathematics Zhejiang Normal University Department of Mathematics University of Wisconsin-MilwaukeeMilwaukee WI 53201 USA Department of Mathematics Zhejiang University

Hausdorff operator is an important operator raised from the dilation on Euclidean space and rooted in the classical summability of number series and Fourier series. It is also connected to many well known operators in real and complex analysis. This article is a survey of some recent developments and extensions on the Hausdorff operator. Particularly, various boundedness properties of the Hausdorff operators, studied recently by our research group, are addressed.

关键词： Hausdorff operator Hardy operator boundedness

Acetylene/argon mixture plasma to build ultrathin carbon bridge of CF_(x)/C/MnO_(2) for high-rate lithium primary battery

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Rare Metals 2024年第6期43卷 2574-2584页

作者： da-Wei Zou Xing-Guang Fu Gao-Bang Chen Yi-fan Liu Bao-shan Wu Xian Jian School of Materials and Energy University of Electronic Science and Technology of ChinaChengdu 611731China Yangtze Delta Region Institute(Huzhou) University of Electronic Science and Technology of ChinaHuzhou 31300lChina

Forming an ultrathin conducting layer on a fluorinated carbon(CFx)surface for reducing severe electrochemical polarization in lithium/fluorinated carbon primary batteries(Li/CF_(x))remains a considerable challenge for achieving batteries with excellent rate ***,CFxwas modified by using acetylene/argon mixture plasma combined with MnO_(2)*** CF_(x)/C/MnO_(2)composite effectively reduced the voltage hysteresis and improved the electrochemical performance of Li/CF_(x).The excellent rate performance of CF_(x)/C/MnO_(2)was due to the high electrochemical activity provided by the atomicscale conductive carbon layer and ultrafine MnO_(2)*** with pristine CF_(x),the charge transfer resistance of the optimized CF_(x)/C/MnO_(2)decreased from 218.5 to 48.2Ω,the discharge rate increased from 2C to 10C,and the power density increased from 3.11 to 13.44 kW·g^(-1),The intrinsic reason for the enhanced rate performance was attributed to the fact that the ultrathin carbon layer acted as a conductive bridge to reduce the voltage hysteresis at the initial stage of the Li/CF_(x)discharge,and the high electrochemical activity of the ultrafine MnO_(2)particles provided a faster lithium-ion diffusion rate.

关键词： C_(2)H_(2)/Ar plasma Fluorinated carbon Lithium primary battery MnO_(2)