Wiener-Luxemburg amalgam spaces
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2021
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909844972240896 |
|---|---|
| author | Peša, Dalimil |
| author_facet | Peša, Dalimil |
| contents | In this paper we introduce the concept of Wiener-Luxemburg amalgam spaces which are a modification of the more classical Wiener amalgam spaces intended to address some of the shortcomings the latter face in the context of rearrangement-invariant Banach function spaces.
We introduce the Wiener-Luxemburg amalgam spaces and study their properties, including (but nor limited to) their normability, embeddings between them and their associate spaces. We also study amalgams of quasi-Banach function spaces and introduce a necessary generalisation of the concept of associate spaces. We then apply this general theory to resolve the question whether the Hardy-Littlewood-Pólya principle holds for all r.i. quasi-Banach function spaces. Finally, we illustrate the asserted shortcomings of Wiener amalgam spaces by providing counterexamples to certain properties of Banach function spaces as well as rearrangement invariance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2102_08743 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Wiener-Luxemburg amalgam spaces Peša, Dalimil Functional Analysis 46E30, 46A16 In this paper we introduce the concept of Wiener-Luxemburg amalgam spaces which are a modification of the more classical Wiener amalgam spaces intended to address some of the shortcomings the latter face in the context of rearrangement-invariant Banach function spaces. We introduce the Wiener-Luxemburg amalgam spaces and study their properties, including (but nor limited to) their normability, embeddings between them and their associate spaces. We also study amalgams of quasi-Banach function spaces and introduce a necessary generalisation of the concept of associate spaces. We then apply this general theory to resolve the question whether the Hardy-Littlewood-Pólya principle holds for all r.i. quasi-Banach function spaces. Finally, we illustrate the asserted shortcomings of Wiener amalgam spaces by providing counterexamples to certain properties of Banach function spaces as well as rearrangement invariance. |
| title | Wiener-Luxemburg amalgam spaces |
| topic | Functional Analysis 46E30, 46A16 |
| url | https://arxiv.org/abs/2102.08743 |