On the non-vanishing of Poincaré series on irreducible bounded symmetric domains

Let [Formula: see text] be an irreducible bounded symmetric domain. Using a vector-valued version of Muić’s integral non-vanishing criterion for Poincaré series on locally compact Hausdorff groups, we study the non-vanishing of holomorphic automorphic forms on [Formula: see text] that are given by Poincaré series of polynomial type and correspond via the classical lift to the Poincaré series of certain K-finite matrix coefficients of integrable discrete series representations of G. We provide an example application of our results in the case when [Formula: see text] and [Formula: see text] with [Formula: see text].