New Atomic Decompositons for Bergman Spaces on the Unit Ball

We derive atomic decompositions and frames for weighted Bergman spaces of several complex variables on the unit ball in the spirit of Coifman, Rochberg, and Luecking. In contrast to our predecessors, we use group theoretic methods, in particular, the representation theory of the discrete series of SU (n, 1) and its covering groups. One of the benefits is a much larger class of admissible atoms.