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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.ORCID iD: 0000-0002-9584-4083
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.
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-12095DOI: 10.4064/sm218-1-4Local ID: b280ba96-7790-4a45-804e-a4e09ce2570eOAI: oai:DiVA.org:ltu-12095DiVA: diva2:985045
Note
Validerad; 2013; 20131125 (andbra)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2017-11-24Bibliographically approved

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