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K-Divisibility and a Theorem of Lorentz and Shimogaki

Colin Bennett and Robert Sharpley
Proceedings of the American Mathematical Society
Vol. 96, No. 4 (Apr., 1986), pp. 585-592
DOI: 10.2307/2046308
Stable URL: http://www.jstor.org/stable/2046308
Page Count: 8
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
K-Divisibility and a Theorem of Lorentz and Shimogaki
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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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