论文标题
与准巴纳赫函数空间及其分子分解相关的库里特空间
Coorbit spaces associated to quasi-Banach function spaces and their molecular decomposition
论文作者
论文摘要
本文提供了与可集成的组表示和准巴纳赫函数空间相关的coorbit空间的独立博览会，同时扩展并简化了先前的工作。主要结果从[Studia Math。，180（3）：237-253，2007]中提供了该理论的扩展，该组承认一个紧凑的，共轭不变的单位邻居到任意（可能是非管状）本地紧凑的组。此外，本文如[J.功能。肛门，280（10）：56，2021]，用于准巴纳赫函数空间的全尺度。该理论是为可能的投影和还原的统一表示而开发的，以便容易适用于良好的函数空间，而无法满足库里特理论的经典假设。与现有的有关准巴纳赫库里特空间的文献相比，我们所有的结果都适用于分析向量的可集成性条件明显较弱，这允许在具体设置中获得尖锐的结果
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
