[1] Bakry D, Baudoin F, Bonnefont M, Chafai D, On gradient bounds for the heat kernel on the Heisenberg group. J Funct Anal, 2008, 255(8): 1905–1938
[2] Beals R, Gaveau B, Greiner P, Hamilton-Jacobi theory and the heat kernel on Heisenberg groups. J Math Pures Appl, 2000, 79: 633–689
[3] Bonfiglioli A, Uguzzoni F. Nonlinear Liouville theorems for some critical problems on H-type groups. J Funct Anal, 2004, 207: 161–215
[4] Cohen A, Dahmen W, Daubechies I, DeVore R. Harmonic analysis of the space BV. Rev Mat Iberoamer-icana, 2003, 19: 235–263
[5] Hsiao L, Li H L. Compressible Navier-Stokes-Poisson equations. Acta Math Sci, 2010, 30B(6): 1937–1948
[6] Eldredge N. Precise estimates for the subelliptic heat kernel on H-type groups. J Math Pures Appl, 2009, 92(1): 52–85
[7] Eldredge N. Gradient estimates for the subelliptic heat kernel on H-type groups. J Funct Anal, 2010, 258(2): 504–533
[8] Folland G. Subelliptic estimates and function spaces on nilpotent Lie groups. Ark. Math., 1975, 13: 161–207
[9] Gaveau B. Principe de moindre action, propagation de la chaleur et estim´ees sous elliptiques sur certains groupes nilpotents. Acta Math, 1977, 139: 95–153
[10] Kaplan A. Fundamental solutions for a class of hypoelliptic PDE generated by composition of quadratic forms. Trans Amer Math Soc, 1980, 258(1): 147–153
[11] Ledoux M. On improved Sobolev embedding theorems. Math Res Lett, 2003, 10: 659–669
[12] Li H Q. Estimation optimale du gradient du semi-groupe de la chaleur sur le groupe de Heisenberg. J Funct Anal, 2006, 236(2): 369–394
[13] Li H Q. Estimations asymptotiques du noyau de la chaleur sur les groupes de Heisenberg. C R Acad Sci Paris, Ser I, 2007, 344(8): 497–502
[14] Li Aobing, Li Yanyan. A Harnack type inequality for some conformally in variant equations on half Euclidean space. Acta Math Sci, 2009, 29B(4): 1105–1112
[15] Randall J. The heat kernel for generalized Heisenberg groups. J Geom Anal, 1996, 6(2): 287–316
[16] N. Varopoulos, Analysis on nilpotent Lie groups. J Funct Anal, 1986, 66: 406–431
[17] Yang Q, Zhu F. The heat kernel on H-type groups. Proc Amer Math Soc, 2008, 136(4): 1457–1464 |