Wiener–Luxemburg amalgam spaces

In this paper we introduce the concept of Wiener–Luxemburg amalgam spaces which are a modification more classical Wiener intended to address some shortcomings latter face in context rearrangement-invariant Banach function spaces. We and study their properties, including (but not limited to) normability, embeddings between them associate also amalgams quasi-Banach necessary generalisation then apply general theory resolve question whether Hardy–Littlewood–Pólya principle holds for all r.i. Finally, illustrate asserted by providing counterexamples certain properties as well rearrangement