Title

K-Divisibility and a Theorem of Lorentz and Shimgaki

Document Type

Article

Subject Area(s)

Mathematics

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 Calder6n's theorem describing the Hardy-Littlewood-Polya relation in terms of substochastic operators (which itself generalizes the classical Hardy Littlewood-Polya result for substochastic matrices) is obtained

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