  In this paper we present an abstract framework for construction of Banach
spaces of distributions from group representations. This generalizes the theory
of coorbit spaces initiated by H.G. Feichtinger and K. Gr\"ochenig in the
1980's. Spaces that can be described by this new technique include the whole
Banach-scale of Bergman spaces on the unit disc. For these Bergman spaces we
show that atomic decompositions can be constructed through sampling. We further
present a wavelet characterization of Besov spaces on the forward light cone.
