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arXiv · 2203.07959

Coorbit spaces associated to quasi-Banach function spaces and their molecular decomposition

Jordy Timo van Velthoven·Felix Voigtlaender
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Abstract

This paper provides a self-contained exposition of coorbit spaces associated to integrable group representations and quasi-Banach function spaces, and at the same time extends and simplifies previous work. The main results provide an extension of the theory in [Studia Math., 180(3):237-253, 2007] from groups admitting a compact, conjugation-invariant unit neighborhood to arbitrary (possibly nonunimodular) locally compact groups. In addition, the present paper establishes the existence of molecular dual frames and Riesz sequences as in [J. Funct. Anal., 280(10):56, 2021] for the full scale of quasi-Banach function spaces. The theory is developed for possibly projective and reducible unitary representations in order to be easily applicable to well-studied function spaces not satisfying the classical assumptions of coorbit theory. Compared to the existing literature on quasi-Banach coorbit spaces, all our results apply under significantly weaker integrability conditions on the analyzing vectors, which allows for obtaining sharp results in concrete settings

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Jordy Timo van Velthoven, Felix Voigtlaender. 2022-03-15. Coorbit spaces associated to quasi-Banach function spaces and their molecular decomposition. https://arxiv.org/abs/2203.07959

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