2021/02/17 by Peša, Dalimil · 2 citations
#46A16 #46E30 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2102.08743
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.