李澎涛，男，1979年8月出生，青岛大学教授， 硕士研究生导师。

学习与进修经历：

1998年9月—2002年6月, 青岛大学师范学院, 获理学学士学位;

2002年9月—2005年6月，青岛大学数学科学学院， 获理学硕士学位;

2005年9月—2009年6月，北京大学数学科学学院，获理学博士学位；

2008年9月—2009年5月，加拿大纽芬兰纪念大学，国家建设高水平大学联合培养博士生；

2009年9月—2010年12月， 澳门大学，从事博士后研究。

工作经历：

2018年11月至今，青岛大学数学与统计学院，教授；

2014年7月-2018年10月，青岛大学数学与统计学院，副教授；

2011年1月—2014年6月，汕头大学数学系，副教授。

学术兼职：

2012年6月—2014年6月，汕头数学会秘书长。

研究方向：

调和分析、偏微分方程

主持的科研项目：

参与的科研项目：

著作\教材\编著\译著\论文集：

[1] 钱涛，李澎涛， Lipschitz边界上的奇异积分和Fourier理论, 现代数学基础丛书 Vol. 167， 科学出版社,  2017 (ISBN 978-7-03-051698-5)。

[2] Tao Qian and Pengtao Li, Singular Integrals and Fourier Theory on Lipschitz Boundaries, Springer,  2019 (ISBN 978-981-13-6499-0)

主要学术论文：(标注"*"为通讯作者)

[69] Jie Cui, Pengtao Li* and Zengjian Lou, Extension of Q type spaces related with weights via s-harmonic equations and applications, to appear in Journal of Mathematical Analysis and Applications, 2022, doi.org/10.1007/s00009-022-02177-1

 [68] Tiantian Dai, Qianjun He, Pengtao Li* and Kai Zhao, On weighted boundedness and compactness of operators generated by fractional heat semigroups related with Schr\"{o}dinger operators, to appear in Annals of Functional Analysis,2022.

 [67] Meimei Shi, Jianfeng Dong and Pengtao Li*, Extension of Q type spaces related with weight functions via convolution operators on Heisenberg groups, to appear in Mathematical Methods in the Applied Sciences, 2022, DOI:10 .1002/mma.8704.

[66] 崔洁，李澎涛*，与对数函数相关的~$Q$ 型空间的调和延拓问题，数学进展，待发表，2022. 

[65] Pengtao Li, Rui Hu and Zhichun Zhai*, Strengthened fractional Sobolev type inequalities in Besov spaces, to appear in Potential Analysis, 2022， doi:10.1007/s11118-022-10030-z.

[64] Pengtao Li, Rui Hu and Zhichun Zhai*,  Fractional Besov Trace/Extension Type Inequalities via the Caffarelli-Silvestre extension, Journal of Geometric Analysis,32 (2022), 236.

[63] Pengtao Li* and Wenchang Sun, Applications of multiresolution analysis in Besov-Q type spaces and Triebel-Lizorkin-Q type spaces, Frontiers of Mathematics in China 17 (2022), 373-435.

[62] Yang Han, Jizhenghuang, Pengtao Li and Yu Liu*, BV spaces and the perimeters related to Schrödinger operators with inverse-square potentials and applications to the rank-one theorem, Nonlinear Analysis TMA, 222 (2022), 112981

[61] Jizheng Huang, Pengtao Li and Yu Liu*, Sobolev and variational capacities in the Hermite setting and their applications,to appear in Mediterranean Journal of Mathematics, 2022

[60] Chunfang Gao and Pengtao Li*, The Herz-boundedness of commutators related to Schr\"{o}dinger operators in the setting of Heisenberg groups,  Bulletin of the Malaysian Mathematical Sciences Society, 145 (2022),  1213-1240

[59] Pengtao Li, Tao Qian, Zhiyong Wang and Chao Zhang*，Regularity of fractional heat semigroup associated with Schrödinger operators，Fractal and Fractional, 2022, 6, 112. https://doi.org/10.3390/ fractalfract6020112

[58] Pengtao Li* and Zhichun Zhai, Application of capacities to space-time fractional dissipative equations II: Carleson measure characterization for $L^q(\mathbb{R}^{n+1}_+,\mu)-$extension, Advances of Nonlinear Analysis,11 (2022), 850-887.

[57] Pengtao Li, Shaoguang Shi, Rui Hu and Zhichun Zhai*, Embeddings of  function            spaces via the Caffarelli-Silvestre extension, capacities and Wolff potentials, Nonlinear Analysis TMA, 217 (2022), 112758

[56] Xuan Chen, Pengtao Li*  and Zengjian Lou, Carleson measures and the boundedness of singular integral of singular integral operators on Q-type spaces related to weights,Annals of Functional Analysis, 13 (2022), doi:10.1007/ s43034-021-00157-2

[55] Pengtao Li*, Ziyong Wang and Kai Zhao, Regularity of the generalized Poisson operators, Journal of the Korean Mathematical Society, 59 (2022), 129-150 .

[54] Qianjun He and Pengtao Li*, On weighted  compactness of commutators         of Schrödinger operators,  Acta  Mathematica Sinica, Series B. 38 (2022), 1015-1040.

[53] Jizheng Huang, Pengtao Li and Yu Liu*, Gaussian BV functions and Gaussian BV capacity on stratified groups, Analysis in Theory and Applications, 37 (2021), 311-329.

[52] Zhiyong Wang, Pengtao Li* and Chao Zhang, Boundedness of operators generated by fractional semigroups associated with Schrödinger operators on Campanato type spaces via $T1$ theorem, Banach Journal of Mathematical Analysis,  (2021)  doi:10.1007/s43037-021-00148-4.

[51] Zhiyong Wang, Tiantian Dai and Pengtao Li*, Characterizations of vanishing Campanato classes related to Schrödinger operators via fractional semigroups on stratified groups, Mathematical Methods in the Applied Sciences, 44 (2021),  10609-10634

[50] 孙传红， 李澎涛， Heisenberg群上与Schrödinger算子相关的Poisson半群的分数阶导数估计，应用数学， 2021，34， 113-122.

[49] Ziyun Jiao, Jizheng Huang∗, Pengtao Li and Yu Liu, Q^{-1}_{\alpha} spaces for Hermite operator and their applications in a class of Hermite-dissipative equations, Journal of Mathematical Analysis and Applications, 500 (2021), 125127.

[48] Fang Han and Pengtao Li*, Characterizations for a class of $Q$-type spaces of several real variables, 数学进展 49 (2020), 195-214.

[47] Jizheng Huang, Pengtao Li* and Yu Liu, Capacity & perimeter from $\alpha$-Hermite bounded variation, Calculus of Variations and PDE, (2020) 59:186, doi: 10.1007/s00526-020-01851-0.

[46] Zhiyong Wang, Chuanhong Sun and Pengtao Li*, Regularities of time-fractional derivatives of semigroups related to Schrödinger operators with applications to Hardy-Sobolev spaces on Heisenberg groups, Journal of Function Spaces,Volume 2020,Article ID 8851287, doi: 10.1155/2020/8851287.

[45] Fang Han and Pengtao Li* , Extension of Besov-Q type spaces via convolution operators with applications,Complex Analysis and Operator Theory 14, 46 (2020).doi: 10.1007/s11785-020-01002-5

[44]  Yixin Wang, Yu Liu, Chuanhong Sun and Pengtao Li*, Carleson measure charac terizations of the Campanato type space associated with Schrödinger operators on stratified  Lie groups, Forum Mathematicum 32 ( 2020), 1337-1373

[43]  Jizheng Huang, Pengtao Li* and Yu Liu, Area integral characterization of Hardy space H-L(1) related to degenerate Schrödinger operators, Advances in Nonlinear Analysis 9 (2020), 1291-1314.

[42]  Jizheng Huang, Pengtao Li*, Yu Liu and Shaoguang Shi, Fractional heat semigroups on metric measure spaces with finite densities and applications to fractional dissipative equations,  Nonlinear Analysis TMA. (2020), 111722.

[41] Jizheng Huang, Pengtao Li, Yu Liu* and Jie Xin, The characterizations of Hardy-Sobolev spaces by fractional square functions  related to Schrö dinger operators, Annales Academiae Scientiarum Fennicae-Mathematica 45 (2020), 607-623.

[40]  Jizheng Huang, Pengtao Li* and Yu Liu, Extension of Campanato-Sobolev type spaces associated with Schrödinger operators, Annals of Functional Analysis 11 (2020), 314-333

[39] Pengtao Li*, Riesz potentials of Hardy-Hausdorff spaces and Q-type spaces, Science China Mathematics 63 (2020), 2017-2036

[38] Fang Han and Pengtao Li *, Harmonic extension of $Q_{\mathcal{K}}$ type spaces via regular wavelets, Complex Vairables and Elliptic Equations 65 (2020), 2008-2025

[37] 李澎涛， 孙文昌，多分辨方法在Besov-Q型空间和Triebel-Lizorkin-Q型空间中的应用，数学进展‏ 48 (2019)， 513-530.

[36] Yixin Wang and Pengtao Li*, Riesz transforms on the Hardy space associated with generalized Schrödinger operators, Journal of Inequalities and Applications  2019 (2019), doi: 10.1186/s13660-019-2126-3

[35]　Yuanyuan Hao, Pengtao Li* and Kai Zhao, Regularities of semigroups, Carleson measures and the characterizations of BMO-type spaces associated with generalized Schrödinger operators, Banach Journal of Mathematical Analysis 13 (2019), 1-25.

[34]Jizheng Huang, Pengtao Li* and Yu Liu, Regularity properties of the heat kernel and area integral characterization of Hardy space H_L^1 related to degenerate Schrödinger operators,Journal of Mathematical Analysis and Applications 466 (2018), 447-470.

[33] Pengtao Li* and Lizhong Peng, Poisson semigroup characterization and the trace theorem of a class of fractional mean oscillation spaces, Mathematical Methods in the Applied Sciences  41 (2018), 3463-3475.

[32] Pengtao Li, Qixiang Yang* and Kai Zhao, Regular wavelets and Triebel-Lizorkin  type oscillation spaces, Mathematical Methods in the Applied Sciences  40 (2017), 6684-6701. .

[31] Qixiang Yang, Tao Qian and Pengtao Li*, Fefferman-Stein decomposition for Q-spaces and micro-local quantities, Nonlinear Analysis TMA.145 (2016), 24-48.

[30] Pengtao Li* and Xin Wan, The boundedness of commutators associated with Schrödinger operators on Herz spaces, Journal of Inequalities and Applications, 2016, 2016(1),1-27.

[29] Qixiang Yang and Pengtao Li*, Regular wavelets, heat semigroup and application to the magneto-hydrodynamic equations with data in critical Triebel-Lizorkin type oscillation spaces, Taiwanese Journal of Mathematics, 20 (2016), 1335-1376.      

[28] Jizheng Huang, Pengtao Li* and Yu Liu, Poisson semigroup, Area function and the characterization of Hardy space associated to degenerate Schrödinger operators, Banach Journal of Mathematical Analysis, 10 (2016), 727-749.

[27] Pengtao Li* and Qixiang Yang, Bilinear estimate on tent type spaces with application to the well-posedness of fluid equations, Mathematical Methods in the Applied Sciences, 39 (2016),4099-4128.

[26] Pengtao Li*,Xin Wan and Chuangyuan Zhang, Schröinger type operators on generalized Morrey spaces, Journal of Inequalities and Applications, 2015, 2015(1), 1-21.

[25] Pengtao Li,Junming Liu and Zengjian Lou*, Analytic version of the critical Q type spaces and their properties, Complex Vairables and Elliptic Equations, 60 (2015), 1327-1345.

[24] Pengtao Li,Heping Liu, Lizhong Peng and Qixiang Yang*, Pseudo-annular decomposition and approximate rate of Calderon-Zygmund operators on Heisenberg group, International Journal of Wavelets, Multiresolution and Information Processing,13, 1550001 (2015),doi: 10.1142/S0219691315500010

[23] Yueping Zhu, Qixiang Yang and Pengtao Li*,Stability and Morrey spaces related to multipliers, Taiwanese Journal of Mathematics,19, (2015), 819-848.

[22] Qixiang Yang and Pengtao Li*,Regular orthogonal basis on Heisenberg group and application to function spaces, Mathematical Methods in the Applied Sciences, 38 (2015), 3163-3182.

[21] Pengtao Li*, Yan Mo and Chuanyuan Zhang, A compactness criterion and application to the commutators associated with Schrödinger operators, Mathematische Nachrichten, 288 (2015), 235-248.

[20] Qixiang Yang, Tao Qian and Pengtao Li*,Spaces of harmonic functions with boundary values in $Q^{\alpha}_{p,q}$,Applicable Analysis, 93 (2014), 2498-2518.

[19] Pengtao Li,Jie Xiao* and Qixiang Yang, Global mild solutions of modified Navier-Stokes equations with small initial data in critical Besov-Q spaces, Electronic Journal of Differential Equations, 2014 (2014), 1-37.

[18] Pengtao Li, Junming Liu and Zengjian Lou*,Integral operators on analytic Morrey spaces, Science China Mathematics Vol.57 (2014), 1961–1974.

[17] Pengtao Li*,Jianhao Lv and Tao Qian,A class of unbounded Fourier multipliers on the unit complex ball，Abstract and Applied Analysis, Vol. 2014, Article ID 602121, 8 pages, 2014.

[16]Pengtao Li*and Tao Qian, Unbounded holomorphic Fourier multipliers on starlike Lipschitz surfaces in the quaternionic space and applications, Nonlinear Analysis TMA, 95 （2014）, 436-449.

[15] Pengtao Liand Qixiang Yang*, Well-posedness of quasi-geostrophic Equations with data in Besov-Q spaces，Nonlinear Analysis TMA. 94 (2014), 243–258.

[14] Pengtao Li, Qixiang Yang* and Yueping Zhu, Wavelets, Sobolev multipliers and application to Schrödinger operators with non-smooth potentials, Abstract and Applied Analysis, 2013 (2013), Article ID 193420, 22 pages.

[13] Pengtao Li and Qixiang Yang*, Wavelets and the well-posedness of incompressible magneto-hydrodynamic equations in Besov type Q-spaces, Journal of Mathematical Analysis and Applications, 405 (2013), 661-686.

[12] 赵凯*，李澎涛，区域上Besov 空间的分子分解及其应用，数学物理学报，2013，33A (5): 926-936.

[11] Pengtao Li* and Lizhong Peng , Lp boundedness of commutator operator associated with Schrödinger operators on Heisenberg group, Acta Mathematica Scientia, Vol. 32B (2012), 568-578.

[10] Pengtao Li and Lizhong Peng*, Compact commutators of Riesz transform associated with Schrödinger operator, Pure and Applied Mathematics Quarterly, 8 (2012), 713-740.

[9] Pengtao Li and Zhichun Zhai*,Riesz transforms on Q-type spaces with application to quasi-geostrophic equation, Taiwanese Journal of Mathematics 16 (2012), 2107-2132.

[8] Pengtao Li*, Ieng Tak Leong and Tao Qian, A class of Fourier multipliers on starlike Lipschitz surfaces, Journal of Functional Analysis, 261 (2011), 1415-1445.

[7] Pengtao Li and Zhichun Zhai*, Several analytic inequality in some Q-spaces, Taiwanese Journal of Mathematics, 15 (2011), 2043-2058.

[6] Pengtao Li and Zhichun Zhai*, Generalized Naiver-Stokes equations with data in local Q-type spaces, Journal of Mathematical Analysis and Applications, 369 (2010), 595-609.

[5] Pengtao Li* and Lizhong Peng, Endpoint estimate for commutator of Riesz transform associated with Schrödinger operator, Bulletin of the Australian Mathematical Society, 82 (2010), 367-389.

[4] Pengtao Li* and Zhichun Zhai Well-posedness and regularity of generalized Naiver-Stokes equations in some critical Q-spaces, Journal of Functional Analysis, 259 (2010), 2457-2519.

[3] Pengtao Li* and Lizhong Peng, The decomposition of product space,Journal of Mathematical Analysis and Applications, 349 (2009), 484-492.

[2] 赵凯*，李澎涛， 朱宏伟，Decompositions of Triebel-Lizorkin spaces on domains,应用数学，2008，21(4)：826-834.

[1] Zihua Guo*,Pengtao Li and Lizhong Peng, Lp boundedness of commutator of Riesz transform associated to Schrödinger operator, Journal of Mathematical Analysis and Applications, 341, (2008), 421-432.

联系方式：

办公地点：青岛市宁夏路308号，青岛大学浮山校区励行楼（西七）223室

办公电话：0532-85953660

E-mail：ptli@qdu.edu.cn