Coorbit space theory for quasi-Banach spaces

We generalize the classical coorbit space theory developed by Feichtinger and Grochenig to quasi-Banach spaces. As a main result we provide atomic decompositions for coorbit spaces defined with respect to quasi-Banach spaces. These atomic decompositions are used to prove fast convergence rates of best n-term approximation schemes. We apply the abstract theory to time-frequency analysis of modulation spaces M-m(p,q), 0 < p, q <= infinity.