Description:
This paper provides a self-contained exposition of coorbit spaces associated with integrable group representations and quasi-Banach function spaces. It extends the theory in [Studia Math., 180(3):237–253, 2007] to locally compact groups that do not necessarily possess a compact, conjugation-invariant unit neighborhood. Furthermore, the present paper establishes the existence of dual molecules of frames and Riesz sequences as in [J. Funct. Anal., 280(10):56, 2021] for the setting of quasi-Banach spaces. To ensure the direct applicability to various well-studied examples, the theory is developed for possibly projective and reducible unitary representations.