𝐾-divisibility and a theorem of Lorentz and Shimogaki

Bennett, Colin; Sharpley, Robert

doi:10.1090/S0002-9939-1986-0826485-7

$K$-divisibility and a theorem of Lorentz and Shimogaki
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by Colin Bennett and Robert Sharpley PDF

Proc. Amer. Math. Soc. 96 (1986), 585-592 Request permission

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.

References

Real interpolation functors

23

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Inequalities

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