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New examples of K-monotone weighted Banach couples
Department of Mathematics and Mechanics, Samara State University.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Department of Mathematical and Statistical Sciences, University of Alberta.
2013 (English)In: Studia Mathematica, ISSN 0039-3223, E-ISSN 1730-6337, Vol. 218, no 1, 55-88 p.Article in journal (Refereed) Published
Abstract [en]

Some new examples of K-monotone couples of the type (X;X(ω)), where X is a symmetric space on [0; 1] and ω is a weight on [0; 1], are presented. Based on the property of ω-decomposability of a symmetric space we show that, if a weight ω changes sufficiently fast, all symmetric spaces X with non-trivial Boyd indices such that the Banach couple (X;X(ω)) is K-monotone belong to the class of ultrasymmetric Orlicz spaces. If, in addition, the fundamental function of X is t1/p for some p ⋯ [1;∞], then X = Lp. At the same time a Banach couple (X;X(ω)) may be K-monotone for some non-trivial w in the case when X is not ultrasymmetric. In each of the cases where X is a Lorentz, Marcinkiewicz or Orlicz space, we find conditions which guarantee that (X;X(ω)) is K-monotone

Place, publisher, year, edition, pages
2013. Vol. 218, no 1, 55-88 p.
Research subject
URN: urn:nbn:se:ltu:diva-12095DOI: 10.4064/sm218-1-4Local ID: b280ba96-7790-4a45-804e-a4e09ce2570eOAI: diva2:985045
Validerad; 2013; 20131125 (andbra)Available from: 2016-09-29 Created: 2016-09-29Bibliographically approved

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Maligranda, Lech
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