刘宇
教授 应用数学系主任
姓名:
刘宇
性别:
男
职称:
教授 应用数学系主任
所在系所:
应用数学系
办公电话:

电子邮件:
ustbmathliuyu@ustb.edu.cn
研究领域:
调和分析和小波分析，偏微分方程，包括与微分算子相关的调和分析问题，非交换调和分析和小波分析，容量和等周长不等式等.


教育经历
2002—2005 北京大学基础数学专业博士研究生，导师：刘和平教授
2014.6—2015.6 加拿大纽芬兰纪念大学数学与统计系访问，合作导师：肖杰教授
工作经历
美国<数学评论>及德国<数学文摘>评论员
科研业绩
论文论著：
自2002年以来，在中国科学(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.等国内外知名的杂志上发表论文40余篇 (http://www.ams.org/mathscinet)，其中SCI检索25篇。以下是发表主要文章的列表（2007年以来）：
[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 operatorsandon 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]刘宇, 薛定谔型算子的交换子的加权有界性, 数学学报， 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 theHeisenberg 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, 数学进展， No.4, 2010. 453-459.
[12]Yu Liu，The Weighted Estimates of the Schr"{o}dinger Operators on the Nilpotent Lie Group，数学研究与评论，No.6, 2010, 1023-1031.
[13]Jun Cao, Yu Liu, Dachun Yang, Hardy spaces H^1_L associated withSchrodinger type operator (-Δ)^2+V^2, Houston J. Math. No.4,2010, 1067-1095. (SCI)
[14] 刘宇，具有非负位势的薛定谔型算子的估计，数学物理学报. 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 Schrödingeroperators 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 ofhomogeneous 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 potentialson nilpotent Lie groups and its applications, Forum Mathematicum, 27(2015),1773-1798.(SCI)
[25]Yu Liu, Jianfeng Dong, The Higher Order Riesz Transform andBMOType 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]陈玉英, 刘宇∗, 王媛媛,与高阶抛物型Schrodinger 算子相关的Riesz变换的Lp 估计,中国科学: 数学，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-JuanSome 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,GuobinHardy 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 YuPoisson 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,GuobinA 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)
科研项目：
1）国家自然科学基金青年基金：与薛定谔算子相关的调和分析问题（项目批准号：**），执行年限为： 2010.1－2012.12，16万，主持。
2）中央科研基本业务费：与微分算子相关的调和分析问题（项目批准号： FRF-BR-11-030B），执行年限为： 2011.5－2013.5，1万，主持。
3）中央科研基本业务费：李群上与积分算子相关的调和分析问题（项目批准号： FRF-BR-13-002），执行年限为： 2013.1－2013.12，10万，主持。
4）2013年入选教育部新世纪优秀人才。经费25万,学校配套15万.共计40万.
5）国家自然科学基金面上项目： Carnot-Caratheodory 空间上若干问题（项目批准号：**），执行年限为： 2017.1－2020.12，48万，主持。