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arXiv · 2508.10825

On the sums of rearrangement-invariant quasi-Banach function spaces and their relationship to amalgams

Dalimil Peša
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Abstract

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.

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Dalimil Peša. 2025-08-14. On the sums of rearrangement-invariant quasi-Banach function spaces and their relationship to amalgams. https://arxiv.org/abs/2508.10825

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