Upcoming Terminology in the World of Function Spaces
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912063871254528 |
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| author | Feichtinger, Hans G |
| author_facet | Feichtinger, Hans G |
| contents | It is the purpose of this article to compare various concepts of ``function spaces''. In particular we compare notions of the concept of Banach Function Spaces (in the spirit of Luxemburg-Zaanen) to the setting of solid BF-spaces as it is widely used in a number of papers in Time-Frequency Analysis or Coorbit Theory.
More recently ball quasi-Banach function spaces come into the picture. In a way this note is a companion to the authors' article entitled ``Choosing Function Spaces in Harmonic Analysis'' (from 2015, February Fourier Talks at the Norbert Wiener Center, Vol.4) and the recent article by E.~Lorist and Z.Nieraeth, entitled ``Banach Function Spaces done right'' (Indag. Math., 2023). We restrict our attention to the Banach space case, avoiding the complications arising in the quasi-Banach case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_04437 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Upcoming Terminology in the World of Function Spaces Feichtinger, Hans G Functional Analysis Classical Analysis and ODEs It is the purpose of this article to compare various concepts of ``function spaces''. In particular we compare notions of the concept of Banach Function Spaces (in the spirit of Luxemburg-Zaanen) to the setting of solid BF-spaces as it is widely used in a number of papers in Time-Frequency Analysis or Coorbit Theory. More recently ball quasi-Banach function spaces come into the picture. In a way this note is a companion to the authors' article entitled ``Choosing Function Spaces in Harmonic Analysis'' (from 2015, February Fourier Talks at the Norbert Wiener Center, Vol.4) and the recent article by E.~Lorist and Z.Nieraeth, entitled ``Banach Function Spaces done right'' (Indag. Math., 2023). We restrict our attention to the Banach space case, avoiding the complications arising in the quasi-Banach case. |
| title | Upcoming Terminology in the World of Function Spaces |
| topic | Functional Analysis Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2410.04437 |