#### 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

#### Publication Info

Published in *Proceedings of the American Mathematical Society*, Volume 96, Issue 4, 1986, pages 585-592.

© Proceedings of the American Mathematical Society 1986, American Mathematical Society

Bennett, C., & Sharpley, R. (1986). K-Divisibility and a Theorem of Lorentz and Shimogaki. *Proceedings of the American Mathematical Society,* *96*(4), 585-592. doi:10.2307/2046308