New examples of K-monotone weighted Banach couples
| Autor: | Astashkin, Sergey V., Maligranda, Lech, Tikhomirov, Konstantin E. |
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| Rok vydání: | 2012 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Some new examples of K-monotone couples of the type (X, X(w)), where X is a symmetric space on [0, 1] and w is a weight on [0, 1], are presented. Based on the property of the w-decomposability of a symmetric space we show that, if a weight w changes sufficiently fast, all symmetric spaces X with non-trivial Boyd indices such that the Banach couple (X, X(w)) is K-monotone belong to the class of ultrasymmetric Orlicz spaces. If, in addition, the fundamental function of X is t^{1/p} for some p \in [1, \infty], then X = L_p. At the same time a Banach couple (X, X(w)) 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 have found conditions which guarantee that (X, X(w)) is K-monotone. Comment: 31 pages |
| Databáze: | arXiv |
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