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. 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. Our results vastly generalize previous work by Coifman and Rochberg. Their atoms correspond to translates of a constant function at a discrete subset of the automorphism group of the domain. In this paper we show that atoms can be obtained as translates of any holomorphic function with rapidly decreasing coefficients (including polynomials). This approach also settles the relation between atomic decompositions for the bounded and unbounded realizations of the domain.