Coorbit space theory for quasi-Banach spaces
Volume 180 / 2007
Studia Mathematica 180 (2007), 237-253
MSC: 42C15, 42C40, 46A16, 46E10, 46E30.
DOI: 10.4064/sm180-3-4
Abstract
We generalize the classical coorbit space theory developed by Feichtinger and Gröchenig 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 $M^{p,q}_m$, $0< p,q \leq \infty $.
