Personal Information

主讲课程

主讲本科课程：实变函数

主讲研究生课程：函数空间理论基础，调和分析基础

学术兴趣及主要研究方向

调和分析，几何分析，偏微分方程

科研项目

1. 调和映照理论中的若干问题，国家自然科学基金青年项目（NSFC11101372），主持

2012/01-2014/12；

2. 曲线上Hilbert变换及相关算子的若干问题，浙江省自然科学基金（LY14A010015），

主持，2014/01-2016/12；

3. 限制性定理，时频分析及其应用，国家自然科学基金面上项目（NSFC 11371316），主要参与人（3），2014/01-2017/12；

4. 中国博士后基金（一等，20060400336），主持，2007/01-2008/06（已结题）.

发表论文和著作

1. Chen, Jiecheng; Zhu, Xiangrong, A note on the strong maximal operator on $R^ n$.

Studia Math. 165 (2004), no. 3, 291--294.

2. Chen, Jiecheng; Zhu, Xiangrong, A note on $BMO$ and its application. J. Math. Anal. Appl.  303 (2005), no. 2, 696--698.

3. Chen, Jiecheng; Zhu, Xiangrong, Boundedness of maximal singular integrals.

Chinese Ann. Math. Ser. B 26 (2005), no. 4, 559--568.

4. Ye, Xiaofeng; Zhu, Xiangrong, A note on certain block spaces on the unit sphere.

Acta Math. Sinica Ser. B 22 (2006), no. 6, 1843--1846.

5. Shen, Gang; Zhu, Xiangrong, Axisymmetric solutions to the $3D$ Euler equations.

Nonlinear Analysis 66 (2007) no. 9, 1938--1948.

6. Zhu, Xiangrong, The existence of weak solutions to the $2D$ Euler equations with initial vorticity in $BMO$. Acta Math. Sinica Ser. B.  23 (2007), no. 10, 1881--1888.                        

7. Chen, Jiecheng; Zhu, Xiangrong, A note on weak type $L^1$ boundedness of CZOs with rough kernels. J. Math. Anal. Appl.  339 (2008), no. 1, 438--453.

8. Chen, Jiecheng; Fan, Dashan; Wang, Meng; Zhu, Xiangrong, $L^p$ bounds for oscillatory hyper Hilbert transform along curves.

Proc.  Amer. Math. Soc. 136 (2008), no. 9, 3145--3153.

9. Zhu, Xiangrong, A remark on vorticity maximal function.

J. Math. Anal. Appl.  340 (2008), no. 2, 1027--1032.

10. Zhu, Xiangrong, Solutions to a certain class of degenerate elliptic equations.

Nonlinear Analysis 71 (2009), no. 1-2,  646--653.

11. Chen, Jiecheng; Fan, Dashan; Zhu, Xiangrong*, Sharp $L^2$ boundedness of the oscillatory hyper Hilbert transform along curves.

Acta Math. Sinica Ser. B.  26 (2010), no. 4, 653--658.

12．Li, Jiayu; Zhu xiangrong, Nonexistence of quasi-harmonic spheres.

Calc. Var. Partial Differential Equations.  37 (2010), no. 3-4, pp. 441-460.

13. Zhu, Xiangrong; Wang, Meng, Liouville theorems for quasi-harmonic functions.

Nonlinear Analysis 73 (2010), 2890-2896.

14．Li Jiayu; Zhu, Xiangrong, Existence of $2D$ Skyrmions.

Math. Z. 268 (2011), no. 1-2, 305–315.

15. Chen, Jiecheng; Fan, Dashan, Wu, Huoxiong; Zhu, Xiangrong,

Oscillatory integrals on unit square along surfaces.

Front. Math. China 6 (2011), no. 1, 49–59.

16．Li Jiayu; Zhu, Xiangrong, Small energy compactness for approximate harmonic mappings. 

Comm. in Contem. Math.  13 (2011), no. 5, 741–763.

17. Li Jiayu; Zhu, Xiangrong, Energy identity for the maps from a surface with tension field bounded in . Pacific J. Math. 260 (2012), no. 1, 181–195.

18. Zhu, Xiangrong, No neck for approximate harmonic maps to the sphere. 

Nonlinear Anal. 75 (2012), no. 11, 4339-4345.

19. Chen, Jiecheng; Zhu, Xiangrong*,  -boundedness of Hilbert transforms along variable curves. J. Math. Anal. Appl. 395 (2012), no. 2, 515–522. 

20. Zhu, Xiangrong; Chen, Jiecheng, Integrability of the general product Hardy operators on the product Hardy spaces. 

Appl. Math. J. Chinese Univ. Ser. B 27 (2012), no. 2, 225–233.

21. Chen, Jiecheng; Zhu, Xiangrong*, Boundedness of multidimensional Hausdorff operators on . J. Math. Anal. Appl. 409 (2014), no. 1, 428–434.