H. G. Feichtinger and K. H. Grochenig described a unified approach to atomic decomposition through integrable group representations in Banach spaces. Studying the properties of a special voice transform, generated by a representation of the Blaschke group over the Bergman space, outlined by the general theory developed by Feichtinger and Grochenig, we obtain that every function from the minimal Mobius invariant space will generate an atomic decomposition in the weighted Bergman spaces. An exaple of multiresolution analysis in the Bergman space will be presented, which is based on a new example of sampling set. The construction is an analogy with the multiresolution analysis generated by the discrete affine wavelets in the space of the square integrable functions on the real line, and in fact is the discretization of the continuous voice transform presented before.