In this talk, I'll give a factorization theorem for the operators on complex hyperbolic space which is closely related to Geller' operator, as well as the CR invariant differential operators on Heisenberg group and CR sphere. By using, among other things, the Kunze-Stein phenomenon on the closed linear group SU(1,n) and Fourier analysis techniques on complex hyperbolic space, we establish the Hardy-Sobolev-Maz'ya inequalities and Trudinger-Moser-Adams inequalities on Siegel domain and the unite ball.