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 , 0 < p,q ≤ ∞.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm180-3-4,
author = {Holger Rauhut},
title = {Coorbit space theory for quasi-Banach spaces},
journal = {Studia Mathematica},
volume = {178},
year = {2007},
pages = {237-253},
zbl = {1122.42018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm180-3-4}
}
Holger Rauhut. Coorbit space theory for quasi-Banach spaces. Studia Mathematica, Tome 178 (2007) pp. 237-253. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm180-3-4/