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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



$K$-divisibility and a theorem of Lorentz and Shimogaki

Authors: Colin Bennett and Robert Sharpley
Journal: Proc. Amer. Math. Soc. 96 (1986), 585-592
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 Calder贸n鈥檚 theorem describing the Hardy-Littlewood-P贸lya relation in terms of substochastic operators (which itself generalizes the classical Hardy-Littlewood-P贸lya result for substochastic matrices) is obtained.

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Article copyright: © Copyright 1986 American Mathematical Society