Education Experiences:
Ph.D., 2010, Beijing Normal University, Beijing, China.
B.S., 2005, Beijing Normal University, Beijing, China.
Working Experiences:
2010-Now, Renmin University of China, Beijing, China.
Research Areas:Harmonic Analysis
Courses: Mathematical Analysis, Real Analysis, Harmonic Analysis.
Papers:
[1] Liguang Liu, Y. Sun and J. Xiao, Quasilinear Laplace equations and inequalities with fractional order, Math. Ann. 388 (2024), no. 1, 1-60
[2] C. Fang and Liguang Liu, Lipschitz-type characterizations of Musielak-Orlicz-Campanato spaces, J. Geom. Anal. 33 (2023), Paper No. 380, 60pp.
[3] C. Fang and Liguang Liu, Pointwise multipliers on Orlicz-Campanato spaces, J. Funct. Anal. 284 (2023), no. 7, Paper No. 109824, 89pp.
[4] Liguang Liu and J. Xiao, Divergence & curl with fractional order, J. Math. Pures Appl. (9), 165 (2022), 190-231.
[5] Liguang Liu, S. Wu, J. Xiao and W. Yuan, The logarithmic Sobolev capacity, Adv. Math. 392 (2021), Paper No. 107993, 88pp.
[6] J. Cao, A. Grigor'yan and Liguang Liu*, Hardy's inequality and Green function on metric measure spaces, J. Funct. Anal. 281 (2021), no. 3, Paper No. 109020, 78 pp.
[7] Liguang Liu and J. Xiao, Fractional Hardy-Sobolev $L^1$-embedding per capacity-duality, Appl. Comput. Harmon. Anal. 51 (2021), 17-55.
[8] Liguang Liu and J. Xiao, Morrey's Fractional Integrals in Campanato-Sobolev's Space and $\mathrm{div}F=f$, J. Math. Pures Appl. (9) 142 (2020), 23-57.
[9] Liguang Liu and J. Xiao, Mean H\"older-Lipschitz potentials in curved Campanato-Radon spaces and equations $(-\Delta)^\frac{\alpha}{2}u=\mu= F_k[u]$, Math. Ann., 375 (2019), no. 3-4, 1045-1077.
[10] A. Bonami, J. Cao, L.D. Ky, Liguang Liu, D. Yang and W. Yuan, Multiplication between Hardy Spaces and their dual spaces, J. Math. Pures Appl. (9) 131 (2019), 130-170.
[11] Z. He, Y. Han, J. Li, Liguang Liu, D. Yang and W. Yuan, A complete real-variable theory of Hardy spaces on spaces of homogeneous type, J. Fourier Anal. Appl. 25 (2019), 2197-2267.
[12] Z. He, Liguang Liu, D. Yang and W. Yuan, New Calder\'on reproducing formulae with exponential decay on spaces of homogeneous type, Sci China Math 62 (2019), no. 2, 283-350.
[13] Liguang Liu, J. Xiao, D. Yang and W. Yuan, Restriction of heat equation with Newton–Sobolev data on metric measure space, Calc. Var. Partial Differential Equations 58 (2019), no. 5, Paper No. 165, 40pp.
[14] Liguang Liu, S. Wu, D. Yang and W. Yuan, New characterizations of Morrey spaces and their preduals with applications to the fractional Laplace equation, J. Differential Equations 266 (2019), no 8, 5118-5167.
[15] Liguang Liu and J. Xiao, A trace law for the Hardy-Morrey-Sobolev space, J. Funct. Anal. 274 (2018), no. 1, 80-120.
[16] Liguang Liu and J. Xiao, Restricting Riesz-Morrey-Hardy potentials, J. Differential Equations, 262 (2017) 5468-5496.
Books/ Monograph:
[1] Liguang Liu, J. Xiao, D. Yang and W. Yuan, Gaussian Capacity Analysis, Lecture Notes in Math. 2225, Springer, Cham, 2018. ix+108 pp.
Services & Awards:
1) Alexander Von Humboldt Research Fellowship, 2013.
2) NSFC, 2012-2014; 2018-2021; 2024-2027
