$K$-divisibility and a theorem of Lorentz and Shimogaki
Authors: Colin Bennett and Robert Sharpley
MSC: Primary 46M35; Secondary 46E30
MathSciNet review: 826485
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Abstract: 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.
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