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Coorbit Space Theory for Quasi-Banach Spaces

Holger Rauhut
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Abstract

We generalize the classical coorbit space theory developed by Feichtinger and Gr"ochenig 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 $M^{p,q}_m$, $0< p,q \leq \infty$.

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Holger Rauhut. 2005-07-22. Coorbit Space Theory for Quasi-Banach Spaces. https://arxiv.org/abs/math/0507466

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