Upcoming Terminology in the World of Function Spaces

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1. Verfasser: Feichtinger, Hans G
Format: Preprint
Veröffentlicht: 2024
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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