Atomic decomposition of real-variable type for Bergman spaces in the unit ball of Cn

In this paper we show that, for any 0 < p _ 1 and _ > 1, every (weighted) Bergman space Ap _(Bn) admits an atomic decomposition of real-variable type. More precisely, for each f 2 Ap _(Bn) there exist a sequence of (p;1)_-atoms ak with compact support and a scalar sequence f_kg such that f = P k _kak in the sense of distribution and Pk j_kjp . kfkp p and moreover, f = Pk _kP_(ak) in Ap_(Bn); where P_ is the orthogonal projection from L2_(Bn) onto A2_(Bn): The proof is constructive and our construction is based on analysis inside the unit ball Bn associated with a quasimetric.