[1] Adachi S, Tanaka K. Trudinger type inequalities in Rn and their best exponents. Proc Amer Math Soc, 2000, 128(7): 2051–2057

[2] Capogna L, Danielli D, Pauls S, Tyson T. An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem. Progress in Mathematics 259. Berlin: Birkhäuser, 2007

[3] Cohn W, Lu G. Best constants for Moser-Trudinger inequalities on the Heisenberg group. Indiana Univ Math J, 2001, 50: 1567–1591

[4] Coulhon T, M¨uller D, Zienkiewicz J. About Riesz transforms on the Heisenberg groups. Math Ann, 1996, 305(2): 369–379

[5] Dong B, Sadek G, Chen Z. On the regularity criteria of the 3D Navier-Stokes equations in critical spaces. Acta Math Sci, 2011, 31B(2): 591–600

[6] Folland G. Subelliptic estimates and function spaces on nilpotent Lie groups. Ark Math, 1975, 13: 161–207

[7] 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

[8] Li Congming, Villavert J. An extension of the Hardy-Littlewood-P´olya inequality. Acta Math Sci, 2011, 31B(6): 2285–2288

[9] Luo G. Improved Gagliardo-Nirenberg inequalities on Heisenberg type groups. Acta Math Sci, 2011, 31B(4): 1583–1590

[10] Lust-Piquard F. A simple-minded computation of heat kernels on Heisenberg groups. Colloq Math, 2003, 97: 233–249

[11] Monti R, Serra Cassano F. Surface measures in Carnot-Carath´eodory spaces. Calc Var Partial Differential Equations, 2001, 13(3): 339–376

[12] Ozawa T. On critical cases of Sobolev inequalities. J Funct Anal, 1995, 127: 259–269

[13] Varopoulos N T, Saloff-Coste L, Coulhon T. Analysis and Geometry on Groups. Cambridge Tracts in Math, Vol 100. Cambridge: Cambridge Univ Press, 1992

[14] Xu C -J. Partial Differential Equations. Basic Lecture for the 12th Chinese National Summer School in Mathematics for Graduate Students, 2007 July-August, Wuhan University, China

[15] Yang Q, Zhu F. The heat kernel on H-type groups. Proc Amer Math Soc, 2008, 136: 1457–1464