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Weighted Oscillation and Variation Inequalities for Singular Integrals and Commutators Satisfying Hrmander Type Conditions

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Acta Mathematica Sinica,English Series 2017年第10期33卷 1397-1420页

作者： Jing ZHANG Huo xiong wu School of Mathematics and Statistics Yili Normal College Yining 835000 P. R. China School of Mathematical Sciences Xiamen University Xiamen 361005 P. R. China

This paper is devoted to investigating the weighted LP-mapping properties of oscillation and variation operators related to the families of singular integrals and their commutators in higher dimension. We establish the weighted type （p, p） estimates for 1 〈 p 〈 ∞ and the weighted weak type （1, 1） estimate for the oscillation and variation operators of singular integrals with kernels satisfying certain HSrmander type conditions, which contain the Riesz transforms, singular integrals with more general homogeneous kernels satisfying the Lipschitz conditions and the classical Dini＇s conditions as model examples. Meanwhile, we also obtain the weighted LP-boundeness for such operators associated to the family of commutators generated by the singular integrals above with BMO（Rd）-functions.

关键词： Oscillation variation singular integrals commutators BMO functions HSrmander con-ditions Muckenhoupt weights

Rough Marcinkiewicz Integrals with Mixed Homogeneity on Product Spaces

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Acta Mathematica Sinica,English Series 2013年第7期29卷 1231-1244页

作者： Feng LIU Huo xiong wu School of Mathematical Sciences Xiamen University

In this paper, the parabolic Marcinkiewicz integral operators on the product spaces R^m × R^n（m, n ≥ 2） are studied. The LP-boundedness for such operators are established under rather weak size conditions of the k... 详细信息

关键词： Marcinkiewicz integrals non-isotropic dilations maximal functions rough kernels product spaces

Heparanase and hepatocellular carcinoma:Promoter or inhibitor?

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World Journal of Gastroenterology 2010年第3期16卷 306-311页

作者： Dong, Shuo wu, xiong-Zhi Tianjin Med Univ Canc Inst & Hosp Zhong Shan Men In Patient Dept Tianjin 300171 Peoples R China

Heparan sulphate proteoglycans (HSPGs) consist of a core protein and several heparan sulphate (HS) side chains covalently linked. HS also binds a great deal of growth factors, chemokines, cytokines and enzymes to the extracellular matrix and cell surface. Heparanase can specially cleave HS side chains from HSPGs. There are a lot of conflicting reports about the role of heparanase in hepatocellular carcinoma (HCC). Heparanase is involved in hepatitis B virus infection and hepatitis C virus infection, the activation of signal pathways, metastasis and apoptosis of HCC. Heparanase is synthesized as an inactive precursor within late endosomes and lysosomes. Then heparanase undergoes proteolytic cleavage to form an active enzyme in lysosomes. Active heparanase translocates to the nucleus, cell surface or extracellular matrix. Different locations of heparanase may exert different activities on tumor progression. Furthermore, enzymatic activities and non-enzymatic activities of heparanase may play different roles during HCC development. The expression level of heparanase may also contribute to the discrepant effects of heparanase. Growth promoting as well as growth inhibiting sequences are contained within the tumor cell surface heparan sulfate. Degrading different HSPGs by heparanase may play different roles in HCC. Systemic studies examining the processing, expression, localization and function of heparanase should shed a light on the role of heparanase in HCC.

关键词： Apoptosis Heparanase Heparan sulphate Hepatocellular carcinoma Infection Metastasis

On Marcinkiewicz Integrals Associated to Compound Mappings with Rough Kernels

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Acta Mathematica Sinica,English Series 2014年第7期30卷 1210-1230页

作者： Feng LIU Huo xiong wu School of Mathematical Sciences Xiamen University

The Lp bounds for the parametric Marcinkiewicz integrals associated to compound mapq pings, which contain many classical surfaces as model examples, are given, where the kernels of our operators are rather rough on the unit sphere as well as in the radial direction. These results substan- tially improve and extend some known results.

关键词： Marcinkiewicz integrals compound mappings rough kernels Fourier transform estimates,extrapolation

The Commutators of Strongly Singular Integral Operators on the Weighted Hardy Spaces

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Acta Mathematica Sinica,English Series 2021年第12期37卷 1909-1920页

作者： Yan Yan HAN Huo xiong wu School of Mathematical Sciences Xiamen UniversityXiamen 361005P.R.China

Let T be a strongly singular Calderon-Zygmund operator and b∈L_(loc)(R^(n)).This article finds out a class of non-trivial subspaces BMO_(ω,p,u)(R^(n))of BMO(R^(n))for certain ω∈A_(1),0 详细信息

Let T be a strongly singular Calderon-Zygmund operator and b∈L_(loc)(R^(n)).This article finds out a class of non-trivial subspaces BMO_(ω,p,u)(R^(n))of BMO(R^(n))for certain ω∈A_(1),0

关键词： Strongly singular Calderon-Zygmund operators commutators Muckenhoupt weights BMO spaces Hardy spaces

On Rough Marcinkiewicz Integrals along Surfaces

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Acta Mathematica Sinica,English Series 2010年第4期26卷 717-730页

作者： Huo xiong wu Jian Kai XU School of Mathematical Sciences Xiamen University Xiamen 361005 P. R. China

In this paper, the authors establish the LP-mapping properties of certain classes of Marcinkiewicz integral operators along surfaces with rough kernels. The results in this paper essentially extend as well as improve ... 详细信息

关键词： Marcinkiewicz integrals surfaces maximal operator Hardy space rough kernel

On Multiple Singular Integrals along Polynomial Curves with Rough Kernels

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Acta Mathematica Sinica,English Series 2008年第2期24卷 177-184页

作者： Huo xiong wu Shan Zhi YANG School of Mathematical Sciences Xiamen University Xiamen 361005 P. R. China

This paper is devoted to the study of a class of singular integral operators defined by polynomial mappings on product domains. Some rather weak size conditions, which imply the Lp boundedness of these singular integral operators as well as the corresponding maximal truncated singular integral operators for some fixed 1〈p〈 ∞,are given.

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

Hydrogeochemical characterization and quality assessment of groundwater using self-organizing maps in the Hangjinqi gasfield area,Ordos Basin,NW China

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Geoscience Frontiers 2021年第2期12卷 781-790页

作者： Chu wu Chen Fang xiong wu Ge Zhu Yuzhe Zhang Department of Water Resources China Institute of Water Resources and Hydropower ResearchBeijing 100083China School of Water Resources and Environment China University of Geosciences(Beijing)Beijing 100083China Center for Advanced Technology and Education(CATE) Florida International UniversityMiamiFL 33174USA

Water resources are scarce in arid or semiarid areas,which not only limits economic development,but also threatens the survival of *** local communities around the Hangjinqi gasfield depend on groundwater sources for water supply.A clear understanding of the groundwater hydrogeochemical characteristics and the groundwater quality and its seasonal cycle is invaluable and indispensable for groundwater protection and *** this study,self-organizing maps were used in combination with the quantization and topographic errors and K-means clustering method to investigate groundwater chemistry *** Piper and Gibbs diagrams and saturation index were systematically applied to investigate the hydrogeochemical characteristics of groundwater from both rainy and dry ***,the entropy-weighted theory was used to characterize groundwater quality and assess its seasonal variability and suitability for drinking *** hydrochemical groundwater dataset,consisting of 10 parameters measured during both dry and rainy seasons,was classified into 6 clusters,and the Piper diagram revealed three hydrochemical facies:Cl-Na type(clusters 1,2 and 3),mixed type(clusters 4 and 5),and HCO3-Ca type(cluster 6).The Gibbs diagram and saturation index suggested thatweathering of rock-forming mineralswere the primary process controlling groundwater chemical composition and validated the credibility and practicality of the clustering ***-thirds of 45 groundwater samples were categorized as excellent-or good-quality and were suitable as drinking *** changes within the same and different clusters from the dry season to the rainy season were detected in approximately 78%of the collected *** main factors affecting the groundwater quality were hydrogeochemical characteristics,and dry season groundwater quality was better than rainy season groundwater *** on this work,such results can be used to investigate the seasonal variation of hy

关键词： Self-organizing maps Seasonal change Entropy-weighted theory Hydrogeochemical characteristics Groundwater quality

Margolus-Levitin speed limit across quantum to classical regimes based on trace distance

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Chinese Physics B 2020年第5期29卷 80-84页

作者： Shao-xiong wu Chang-Shui Yu School of Science North University of ChinaTaiyuan 030051China School of Physics Dalian University of TechnologyDalian 116024China

The classical version of Mandelstam-Tamm speed limit based on theWigner function in phase space was reported by Shanahan et al.[***.120070401(2018)].We present the Margolus-Levitin speed limit across the quantumto-classical transition in phase space based on the trace *** Margolus-Levitin speed limit is set by the Schatten L1 norm of the generator of time-dependent evolution for both the quantum and classical *** an example,the time-dependent harmonic oscillator is considered to illustrate the result.

关键词： quantum speed limit Wigner function phase space Margolus-Levitin bound