$K$-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
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Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 96 (1986), 585-592
- MSC: Primary 46M35; Secondary 46E30
- DOI: https://doi.org/10.1090/S0002-9939-1986-0826485-7
- MathSciNet review: 826485