Coorbit spaces associated to quasi-Banach function spaces and their molecular decomposition
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866916134304874496 |
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| author | van Velthoven, Jordy Timo Voigtlaender, Felix |
| author_facet | van Velthoven, Jordy Timo Voigtlaender, Felix |
| contents | 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 |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_07959 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Coorbit spaces associated to quasi-Banach function spaces and their molecular decomposition van Velthoven, Jordy Timo Voigtlaender, Felix Functional Analysis Classical Analysis and ODEs 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 |
| title | Coorbit spaces associated to quasi-Banach function spaces and their molecular decomposition |
| topic | Functional Analysis Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2203.07959 |