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  • 姓名:

    劉宇
  • 性別:

  • 職稱:

    教授
  • 職務:

    副院長
  • 所在係所:

    應用數學係
  • 辦公電話:

    010-62332891
  • 電子郵件:

    ustbmathliuyu@ustb.edu.cn
  • 研究領域:

    調和分析和小波分析,偏微分方程,包括與微分算子相關的調和分析問題,非交換調和分析和小波分析,容量和等周長不等式等.

教育經曆

    2002—2005 北京大學基礎數學專業博士研究生,導師:劉和平教授
    2014.6—2015.6 加拿大紐芬蘭紀念大學數學與統計係訪問學者,合作導師:肖傑教授

工作經曆

    美國<數學評論>及德國<數學文摘>評論員

科研業績

    論文論著:
    自2002年以來,在中國科學(英文版), PAMS, Commun. Pure Appl. Anal., J. Math. Anal. Appl., Potential Analysis, Math. Nachr.,Forum Math., J.Goem.Anal, Banach J.Math.Anal, Dynamics of PDE.等國內外知名的雜誌上發表論文40餘篇 (http://www.ams.org/mathscinet),其中SCI檢索25篇。以下是發表主要文章的列表(2007年以來):
    [1] Heping Liu, Yu Liu, Refinable functions on the Heisenberg group, Commun. Prue  Appl. Anal. 3(2007), 775-787.(SCI)
    [2] Yu Liu,  Mei Yu, Lipschitz continuity of refinable functions on the Heisenberg group, J. Math. Anal. Appl.  338(2008), 1081-1091.(SCI)
    [3] Yu Liu, The weighted estimates for the operators點擊瀏覽下一頁 and 點擊瀏覽下一頁 on the stratified Lie group G, J. Math. Anal. Appl.  349(2009), 235-244. (SCI) 
    [4]Heping Liu, Yu Liu, Haihui Wang, Multiresolution analysis, self-similar tilings and Haar wavelets on the Heisenberg group,  Acta Math. Sci.   No.5,  2009, 1251-1266.  (SCI) 
    [5]劉宇, 薛定諤型算子的交換子的加權點擊瀏覽下一頁有界性,  數學學報, No.6, 2009, 1091-1100.
    [6] Jizheng Huang, Yu Liu, Some characterizations of weighted Hardy spaces.  Jour. Math.  Anal. Appl., Vol. 363,  2010, 121-127. (SCI)
    [7] Yu Liu, Lizhong Peng, Wavelets with vanishing moments on the Heisenberg group, International Journal of Wavelets, Multiresolution and Information Processing,  No.1, 2010, 1-18. (SCI) 
    [8] Yu Liu, L^p estimates for Schrodinger type operators on the Heisenberg  group.  Journal of Korean Mathematical Society. No.3,  2010,425-443.  (SCI) 
    [9] Yu Liu, Jizheng Huang, Dongmei Xie, Some estimates  of    Schrodinger type  operators on  the Heisenberg group,  Archiv der Mathematik. No.3,  2010, 255-264.  (SCI) 
    [10] Yu Liu, Jianfeng Dong, Some estimates  of higher order  Riesz transform related   to  Schrodinger type  operators. Potential Analysis, No.1, 2010, 41-55. (SCI) 
    [11]Yu Liu, Riesz transform associated with Schrodinger operators on the Heisenberg group, 數學進展, No.4, 2010. 453-459.
    [12]Yu Liu,The Weighted Estimates of the Schr"{o}dinger Operators on the Nilpotent Lie Group,數學研究與評論,No.6, 2010, 1023-1031.
    [13]Jun Cao, Yu Liu, Dachun Yang, Hardy spaces H^1_L associated with  Schrodinger type operator (-Δ)^2+V^2, Houston J. Math. No.4, 2010, 1067-1095. (SCI) 
    [14] 劉宇,具有非負位勢的薛定諤型算子的估計,數學物理學報. 2011. No.3,611-619.
    [15]Liu yu, Huang jizheng, Lp estimates for the Schr¨odinger type operators, Appl. Math. J. Chinese Univ.series B, No.4, 2011, 412-424.(SCI) 
    [16] Lin Chincheng, Lin yingchieh, Liu Heping, Liu Yu, Bilinear operators associated with Schrödinger operators, Studia Math.  205(3), 2011, 281-295. (SCI) 
    [17] Jianfeng Dong, Yu Liu,The higher order Riesz transform and $BMO$ type space associated to Schr"{o}dinger operators, Math. Nachr. 285(4), 2012,486-496. (SCI)
    [18]Yu Liu,Commutators of BMO functions and degenerate Schrödinger operators with certain nonnegative potentials, Monatsh Math. Vol. 165, 2012, 41-56. (SCI) 
    [19]Yu Liu, Jianfeng Dong, Some estimates for the Schr¨odinger type operators with nonnegative potentials, Archiv der Mathematik. Vol.98, 2012, 467-475. (SCI) 
    [20]Yu Liu, Lijuan Wang, Jianfeng Dong, Commutators of Higher Order Riesz Transform Associated withSchrödinger Operators,Jour.Function spaces Appl. Volume 2013, Article ID 842375, 15 pages. (SCI)   
    [21]Yu  Liu, Jizheng Huang, JIanfeng Dong, Commutators of Calder´on-Zygmund operatorsrelated to admissible functions on spaces of homogeneous type and applications toSchr¨odinger operators, Sci.China Math. 2013, 56(9): 1895-1913.  (SCI) 
    [22]Jizheng Huang, Yu Liu, The boundedness of multilinear Calderon-Zygmund operators on Hardy spaces, PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2013.3(123), 383-392.(SCI) 
    [23] Yu Liu, Jizheng Huang, Jianfeng Dong, Lp estimates for higher-order parabolic Schrodinger operatorswith certain nonnegative potentials, Bull. Malays. Math. Sci. Soc.37(2014),no.1,153–164. (SCI) 
    [24] Yu Liu, Jizheng Huang, Jianfeng Dong, An estimate on the heat kernel ofSchrödinger operators with non-negative potentials on nilpotent Lie groups and its applications, Forum Mathematicum, 27(2015), 1773-1798.(SCI)  
    [25]Yu Liu, Jianfeng Dong, The Higher Order Riesz Transform and BMO Type Space Associated with Schrödinger Operators on Stratified Lie Groups, Journal of Function Spaces and Applications Volume 2013 (2013), Article ID 483951, 13 pages.(SCI)  
    [26] Yu Liu, Jielai Sheng, and LijuanWang, Weighted Endpoint Estimates for Commutators of RieszTransforms Associated with Schrödinger Operators. Abstract and Applied Analysis,Volume 2013, Article ID 281562, 10 pages.(SCI)  
    [27]Yu Liu; Jielai Sheng, Some estimates for commutators of Riesz transforms associated with Schrödinger operators. J.Math.Anal.Appl.419(2014),no.1, 298–328.(SCI) 
    [28]Jizheng Huang; Yu Liu; Molecular Characterization of Hardy Spaces Associated with Twisted Convolution. J.Funct.Spaces2014,Art. ID 326940, 6 pp.(SCI) (SCI) 
    [29]陳玉英, 劉宇∗, 王媛媛,與高階拋物型Schrodinger 算子相關的Riesz變換的Lp 估計,中國科學: 數學,2014 年第44 卷第5 期: 435-446.
    [30]Yu Liu, Lijuan Wang, Boundedness for Riesz transform associated with Schrodinger operators and its commutator on weighted Morrey spaces related to certain nonnegative potentials,JOURNAL OF INEQUALITIES AND APPLICATIONS, 2014.(SCI) 
    [31] Liu, Yu; Xie, Wenjiang; Riesz transform related to a Schrödinger type operator on the Heisenberg group. Georgian Math. J.  22  (2015),  no. 3, 397–407. (SCI) 
    [32] Yu Liu, Yuzhao Wang, Jie Xiao, Nonnegative solutions of $|g|^{gamma}_{mathbb{H}^n}u^ple(-Delta_{mathbb{H}^n})^{frac{alpha}{2}} u$ on Heisenberg group $mathbb{H}^n$,   Dynamics of PDE. (2015),no.4,379–403. (SCI)

    [33]  Liu,Yu;Zhang,Jing;Sheng,Jie-Lai;Wang,Li-Juan Some estimates for commutators of Riesz transform associated with Schrödinger type operators.Czechoslovak Math.J.66(141) (2016),no,1, 169–191. (SCI)
    [34]  Liu Yu,Tang,Guobin  Hardy type estimates for Riesz transforms associated with Schrödinger operators on the Heisenberg group. Anal.Theory Appl.32(2016),no.1,78–89.
    [35] Huang,Jizheng;Li,Pengtao;Liu Yu Poisson semigroup, area function, and the characterization of Hardy space associated to degenerate Schrödinger operators. Banach J.Math.Anal.10(2016),no.4,727–749. (SCI)
    [36]  Liu Yu;Tang,Guobin  A note for Riesz transforms associated with Schrödinger operators on the Heisenberg group. Anal.Math.Phys.7(2017),no.1, 31–45. (SCI)
    [37]  Liu, Yu; BV Capacity on Generalized Grushin Plane.J.Geom.Anal.27(2017),no.1,409–441. (SCI)
    科研項目:
    1)國家自然科學基金青年基金:與薛定諤算子相關的調和分析問題(項目批準號:10901018),執行年限為: 2010.1-2012.12,16萬,主持。
    2)中央科研基本業務費:與微分算子相關的調和分析問題(項目批準號: FRF-BR-11-030B),執行年限為: 2011.5-2013.5,1萬,主持。
    3)中央科研基本業務費:李群上與積分算子相關的調和分析問題(項目批準號: FRF-BR-13-002),執行年限為: 2013.1-2013.12,10萬,主持。
    4)2013年入選教育部新世紀優秀人才。經費25萬,學校配套15萬.共計40萬.
    5)國家自然科學基金麵上項目: Carnot-Caratheodory 空間上若幹問題(項目批準號:11671031),執行年限為: 2017.1-2020.12,48萬,主持。

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