On the sums of rearrangement-invariant quasi-Banach function spaces and their relationship to amalgams
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915599659040768 |
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| author | Peša, Dalimil |
| author_facet | Peša, Dalimil |
| contents | In this paper we consider the properties of sums of rearrangement-invariant quasi-Banach function spaces, with the focus being on rearrangement-invariance and the Fatou property. In our first main result, we show that the quasinorm of the sum is in many cases equivalent to a rearrangement-invariant quasinorm by providing a weaker version of the Luxemburg-type representation. In our second main result, we show that the sum can be in some cases characterised as a Wiener--Luxemburg amalgam of the two constituent spaces, thus providing a sufficient condition for the sum being a rearrangement-invariant quasi-Banach function space. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_10825 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the sums of rearrangement-invariant quasi-Banach function spaces and their relationship to amalgams Peša, Dalimil Functional Analysis 46E30 In this paper we consider the properties of sums of rearrangement-invariant quasi-Banach function spaces, with the focus being on rearrangement-invariance and the Fatou property. In our first main result, we show that the quasinorm of the sum is in many cases equivalent to a rearrangement-invariant quasinorm by providing a weaker version of the Luxemburg-type representation. In our second main result, we show that the sum can be in some cases characterised as a Wiener--Luxemburg amalgam of the two constituent spaces, thus providing a sufficient condition for the sum being a rearrangement-invariant quasi-Banach function space. |
| title | On the sums of rearrangement-invariant quasi-Banach function spaces and their relationship to amalgams |
| topic | Functional Analysis 46E30 |
| url | https://arxiv.org/abs/2508.10825 |