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.
Publication Source (Journal or Book title)
Indiana University Mathematics Journal
Christensen, J., Gröchenig, K., & Ólafsson, G. (2017). New atomic decompositons for Bergman spaces on the unit ball. Indiana University Mathematics Journal, 66 (1), 205-235. https://doi.org/10.1512/iumj.2017.66.5964