Mean oscillation, weighted Bergman spaces, and Besov spaces on the Heisenberg group and atomic decomposition (Q810204)

In the present paper the notion of mean oscillation spaces are extended for the Heisenberg group \(H_ n\). There are established some equivalent norms for these spaces. It is given an atomic decomposition of the boundary functionals of weighted holomorphic Bergman spaces. It is proved that the Szegö kernels are inside any oscillation space and that the Cauchy-Szegö projection from the atomic spaces to the weighted Bergman spaces are bounded.