Sharp Hardy-Sobolev-Maz'ya, Adams and Hardy-Adams inequalities on the Siegel domains and complex hyperbolic spaces

The aim of this paper is to establish higher order Poincaré-Sobolev, Hardy-Sobolev-Maz'ya, Adams and Hardy-Adams inequalities on Siegel domains complex hyperbolic spaces using the method Helgason-Fourier analysis spaces. Firstly, we give a factorization theorem for operators space which closely related Geller's operator, as well CR invariant differential Heisenberg group sphere. (See Theorem 1.3.) Secondly, by using, among other things, Kunze-Stein phenomenon closed linear SU(1,n) techniques spaces, Hardy-Sobolev-Maz'ya inequality domain Un unit ball BCn. 1.4, 1.5.) Finally, sharp type Sobolev any positive fractional 1.9, 1.10, 1.12.) prove considerably more difficult than in case real should be its independent interest sphere therein.