科研業(yè)績(jī)
論文論著：
自2002年以來(lái)，在中國(guó)科學(xué)(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(guó)內(nèi)外知名的雜志上發(fā)表論文40余篇 (http://www.ams.org/mathscinet)，其中SCI檢索25篇。以下是發(fā)表主要文章的列表（2007年以來(lái)）：
[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
and
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(quán)
有界性, 數(shù)學(xué)學(xué)報(bào)， 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(shù)學(xué)進(jìn)展， No.4, 2010. 453-459.
[12]Yu Liu，The Weighted Estimates of the Schr"{o}dinger Operators on the Nilpotent Lie Group，數(shù)學(xué)研究與評(píng)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(fù)位勢(shì)的薛定諤型算子的估計(jì)，數(shù)學(xué)物理學(xué)報(bào). 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(guān)的Riesz變換的Lp 估計(jì),中國(guó)科學(xué): 數(shù)學(xué)，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(xiàng)目：
1）國(guó)家自然科學(xué)基金青年基金：與薛定諤算子相關(guān)的調(diào)和分析問(wèn)題（項(xiàng)目批準(zhǔn)號(hào)：10901018），執(zhí)行年限為： 2010.1－2012.12，16萬(wàn)，主持。
2）中央科研基本業(yè)務(wù)費(fèi)：與微分算子相關(guān)的調(diào)和分析問(wèn)題（項(xiàng)目批準(zhǔn)號(hào)： FRF-BR-11-030B），執(zhí)行年限為： 2011.5－2013.5，1萬(wàn)，主持。
3）中央科研基本業(yè)務(wù)費(fèi)：李群上與積分算子相關(guān)的調(diào)和分析問(wèn)題（項(xiàng)目批準(zhǔn)號(hào)： FRF-BR-13-002），執(zhí)行年限為： 2013.1－2013.12，10萬(wàn)，主持。
4）2013年入選教育部新世紀(jì)優(yōu)秀人才。經(jīng)費(fèi)25萬(wàn),學(xué)校配套15萬(wàn).共計(jì)40萬(wàn).
5）國(guó)家自然科學(xué)基金面上項(xiàng)目： Carnot-Caratheodory 空間上若干問(wèn)題（項(xiàng)目批準(zhǔn)號(hào)：11671031），執(zhí)行年限為： 2017.1－2020.12，48萬(wàn)，主持。
