Coorbit Space Theory for Quasi-Banach Spaces

TL;DR

This paper extends coorbit space theory to quasi-Banach spaces, providing atomic decompositions and demonstrating fast approximation schemes, with applications to time-frequency analysis of modulation spaces.

Contribution

It introduces a generalized coorbit space framework for quasi-Banach spaces, including atomic decompositions and convergence results, expanding the applicability of the theory.

Findings

Atomic decompositions for quasi-Banach coorbit spaces

Fast convergence rates of n-term approximation schemes

Application to time-frequency analysis of modulation spaces

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 $M^{p,q}_m$, $0< p,q \leq \infty$.