New atomic decompositions of Bergman spaces on bounded symmetric domains

Abstract

We provide a large family of atoms for Bergman spaces on irreducible bounded symmetric domains. This vastly generalizes results by Coifman and Rochberg from 1980. The atomic decompositions are derived using the holomorphic discrete series representations for the domain, and the approach is inspired by recent advances in wavelet and coorbit theory. This approach also settles the relation between atomic decompositions for the bounded and unbounded realizations of the domain.