陆国震,教授,调和分析专家。1991年获得美国罗格斯大学博士学位,1991~1993年为美国加州理工学院博士后。2002年起至今为美国韦恩州立大学教授,并担任包括《非线性分析-理论,方法及其应用》,《数学学报英文版》等多家国际数学杂志编委。 研究领域:调和分析和几何不等式及其在偏微分方程和几何分析中的应用。多年来从事于多参数调和分析理论(包括多参数哈代空间和奇异积分算子理论,多参数多线性傅立叶乘子,拟微分算子,傅立叶积分算子的有界性等),分析中几何不等式的最佳常数与极值函数以及在偏微分方程与几何分析中的应用方向的研究。
目前从事调和分析及其在偏微分方程和几何分析中的应用的研究工作. 主要研究方向为几何不等式(Poincare, Sobolev, Moser-Trudinger, Hardy-Littlewood-Sobolev inequalities)及其在偏微分方程中的应用, Heisenberg群上的分析及其次椭园偏微分方程, 多参数调和分析(包括Littlewood-Paley理论, 多参数Hardy空间, 奇异积分算子的有界性等).
1. Han, Yongsheng; Li, JI Li; Lu, Guozhen, Duality of multiparameter Hardy spaces H^p on spaces of homogeneous type, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5), Vol. IX (2010), 645-685.
2. Hofmann, Steve, Lu, Guozhen Lu, Mitrea, Dorina, Mitrea, Marius, Yan, Lixin; Hardy spaces associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates, Memoires of American Mathematical Society, 2011.
3. Han, Xiaolong; Lu, Guozhen A geometric covering lemma and nodal sets of eigenfunctions, Mathematical Research Letters, 18(2), 2011, 337-352.
4. Lu, Guozhen; Wang, Peiyong On the uniqueness of a solution of a two-phase free boundary problem. J. Funct. Anal. 258 (2010), no. 8, 2817-2833.
5. Lu, Guozhen; Yang, Yunyan Adams' inequalities for bi-Laplacian and extremal functions in dimension four. Adv. Math. 220 (2009), no. 4, 1135-1170.
6. Lu, Guozhen; Wang, Peiyong A PDE perspective of the normalized infinity Laplacian. Comm. Partial Differential Equations 33 (2008), no. 10-12, 1788-1817.
7. Lu, Guozhen; Wang, Peiyong Inhomogeneous infinity Laplace equation. Adv. Math. 217 (2008), no. 4, 1838-1868
8. Juutinen, Petri; Lu, Guozhen; Manfredi, Juan J.; Stroffolini, Bianca Convex functions on Carnot groups. Rev. Mat. Iberoam. 23 (2007), no. 1, 191-200
9. Cohn, William S.; Lu, Guozhen; Wang, Peiyong Sub-elliptic global high order Poincaré inequalities in stratified Lie groups and applications. J. Funct. Anal. 249 (2007), no. 2, 393-424.
10. Huang, Qingbo; Lu, Guozhen On a priori C^{1,α} and W^{2,p} estimates for a parabolic Monge-Ampère equation in the Gauss curvature flows. Amer. J. Math. 128 (2006), no. 2, 453-480.
11. Cohn, William S.; Lu, Guozhen Sharp constants for Moser-Trudinger inequalities on spheres in complex space C^n. Comm. Pure Appl. Math. 57 (2004), no. 11, 1458-1493.