Jun CAO

I am a professor in the Department of Applied Mathematics and a member of the analysis and geometry research group.  My research area is harmonic analysis and its applications. 

I teach the following courses in the past two years. 

2023-2024（1）

1. 《Mathematical Analysis I》,     undergraduate students.

2. 《Topology》,                undergraduate students

3. 《Real Analysis》,             Master's students

4. 《Discipline Frontier Lecture》，   doctoral students

2022-2023 (2) 

1. 《Mathematics Major Introduction》,           undergraduate students

2. 《Selected Lectures on Mathematical Analysis》， undergraduate students

3. 《Academic Writing》，                  Master's Student 

Host academic conferences

Workshop on Harmonic Analysis and Its Application in Hangzhou 2023

Workshop on Harmonic Analysis and Its Applications in Hangzhou 2021

Research Area：

My research area is Harmonic Analysis and Its Applications. My main interests focus on the following three topics.

1. Harmonic analysis and operator theory.

• Gaussian estimates for heat kernels of higher order Schrödinger operators with potentials in generalized Schechter classes, with Liu, Yu; Yang, Dachun; Zhang, Chao J. Lond. Math. Soc. (2) 106 (2022), no. 3, 2136–2192. 

• Weighted local Orlicz-Hardy spaces on domains and their applications in inhomogeneous Dirichlet and Neumann problems，with Chang, Der-Chen; Yang, Dachun; Yang, Sibei, Trans. Amer. Math. Soc. 365 (2013), no. 9, 4729–4809. 

• Local Hardy spaces associated with inhomogeneous higher order elliptic operators, with Mayboroda, Svitlana; Yang, Dachun Anal. Appl. (Singap.) 15 (2017), no. 2, 137–224. 

• Maximal function characterizations of Hardy spaces associated to homogeneous higher order elliptic operators, with Mayboroda, Svitlana; Yang, Dachun Forum Math. 28 (2016), no. 5, 823–856. 

• Hardy spaces  HpL(Rn)  associated with operators satisfying  k -Davies-Gaffney estimates , with Yang, DaChun Sci. China Math. 55 (2012), no. 7, 1403–1440. 

• Non-tangential maximal function characterizations of Hardy spaces associated with degenerate elliptic operators, with Zhang, Junqiang; Jiang, Renjin; Yang, Dachun Canad. J. Math. 67 (2015), no. 5, 1161–1200. 

• Hardy spaces associated with a pair of commuting operator, with; Fu Zunwei; Jiang, Renjin; Yang, Dachun Forum Math. 27 (2015), no. 5, 2775–2824. 

• Weak Hardy spaces  WHpL(Rn)  associated to operators satisfying  k -Davies-Gaffney estimates, with Chang, Der-Chen; Wu, Huoxiong; Yang, Dachun J. Nonlinear Convex Anal. 16 (2015), no. 7, 1205–1255. 

• Estimates for second-order Riesz transforms associated with magnetic Schrödinger operators on Musielak-Orlicz-Hardy spaces, with Chang, Der-Chen; Yang, Dachun; Yang, Sibei Appl. Anal. 93 (2014), no. 11, 2519–2545. 

• Boundedness of second order Riesz transforms associated to Schrödinger operators on Musielak-Orlicz-Hardy space, with Chang, Der-Chen; Yang, Dachun; Yang, Sibei Commun. Pure Appl. Anal. 13 (2014), no. 4, 1435–1463. 

• Musielak-Orlicz-Hardy spaces associated with operators satisfying reinforced off-diagonal estimates , with Bui, The Anh; Ky, Luong Dang; Yang, Dachun; Yang, Sibei Anal. Geom. Metr. Spaces 1 (2013), 69–129. 

• Weighted Hardy spaces associated with operators satisfying reinforced off-diagonal estimates, with The Anh Bui; Ky, Luong Dang; Yang, Dachun; Yang, Sibei Taiwanese J. Math. 17 (2013), no. 4, 1127–1166. 

• Boundedness of generalized Riesz transforms on Orlicz-Hardy spaces associated to operators , with Chang, Der-Chen; Yang, Dachun; Yang, Sibei Integral Equations Operator Theory 76 (2013), no. 2, 225–283. 

• Endpoint boundedness of Riesz transforms on Hardy spaces associated with operators, with Yang, Dachun; Yang, Sibei Rev. Mat. Complut. 26 (2013), no. 1, 99–114. 

• Hardy spaces  H1L(Rn)  associated to Schrödinger type operators  (−Δ)2+V2, with Liu, Yu; Yang, Dachun Houston J. Math. 36 (2010), no. 4, 1067–1095.

2. Thery of function space.

• Multiplication between Hardy spaces and their dual spaces, with Bonami, Aline; Ky, Luong Dang; Liu, Liguang; Yang, Dachun; Yuan, Wen J. Math. Pures Appl. (9) 131 (2019), 130–170. 

• Riesz transform characterizations of Musielak-Orlicz-Hardy spaces, with Chang, Der-Chen; Yang, Dachun; Yang, Sibei Trans. Amer. Math. Soc. 368 (2016), no. 10, 6979–7018. 

• Intrinsic structures of certain Musielak-Orlicz Hardy spaces, with Liu, Liguang; Yang, Dachun; Yuan, Wen J. Geom. Anal. 28 (2018), no. 4, 2961–2983. 

• Local potential operator and uniform resolvent estimate for generalized Schrödinger operator in Orlicz spaces, with Dou, Xiaoshen; Gao, Mengyao; Jin, Yongyang Math. Nachr. 296 (2023), no. 10, 4533–4558. 

• Boundedness of fractional integrals on weighted Orlicz-Hardy spaces, with Chang, Der-Chen; Yang, Dachun; Yang, Sibei Math. Methods Appl. Sci. 36 (2013), no. 15, 2069–2085. 

• Real interpolation of weighted tent spaces, with Chang, Der-Chen; Fu, Zunwei; Yang, Dachun Appl. Anal. 95 (2016), no. 11, 2415–2443. 

• Bilinear decompositions of products of local Hardy and Lipschitz or BMO spaces through wavelets, with Ky, Luong Dang; Yang, Dachun Commun. Contemp. Math. 20 (2018), no. 3, 1750025, 30 pp.

3. Heat kernel and related questiosns.

• Heat kernels and Besov spaces associated with second order divergence form elliptic operators, with Grigor'yan, Alexander J. Fourier Anal. Appl. 26 (2020), no. 1, Paper No. 3. 

• Hardy's inequality and Green function on metric measure spaces, with  Grigor'yan, Alexander; Liu, Liguang J. Funct. Anal. 281 (2021), no. 3, Paper No. 109020, 78 pp. 

• Heat kernels and Besov spaces on metric measure spaces, with Grigor'yan, Alexander J. Anal. Math. 148 (2022), no. 2, 637–680. 

• Characterizations of weighted Hardy-Rellich inequalities and their applications, with Jin, Yongyang; Shen, Shoufeng; Wu, Yurong Math. Inequal. Appl. 23 (2020), no. 3, 873–893.