Bennett, Colin; Sharpley, Robert K-divisibility and a theorem of Lorentz and Shimogaki. (English) Zbl 0607.46046 Proc. Am. Math. Soc. 96, 585-592 (1986). The Brudnyi-Krugljak theorem on the K-divisibility of Gagliardo couples is derived by elementary means from earlier results of Lorentz-Shimogaki on equimeasurable rearrangements of measurable functions. A slightly stronger form of Calderón’s theorem describing the Hardy-Littlewood- Pólya relation in terms of substochastic operators (which itself generalizes the classical Hardy-Littlewood-Pólya result for substochastic matrices) is obtained. Cited in 6 Documents MSC: 46M35 Abstract interpolation of topological vector spaces 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) Keywords:Brudnyi-Krugljak theorem on the K-divisibility of Gagliardo couples; equimeasurable rearrangements of measurable functions; Calderón’s theorem describing the Hardy-Littlewood-Pólya relation in terms of substochastic operators PDFBibTeX XMLCite \textit{C. Bennett} and \textit{R. Sharpley}, Proc. Am. Math. Soc. 96, 585--592 (1986; Zbl 0607.46046) Full Text: DOI