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arXiv · 1206.1244

New examples of K-monotone weighted Banach couples

Sergey V. Astashkin·Lech Maligranda·Konstantin E. Tikhomirov
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Abstract

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.

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Sergey V. Astashkin, Lech Maligranda, Konstantin E. Tikhomirov. 2012-06-06. New examples of K-monotone weighted Banach couples. https://arxiv.org/abs/1206.1244

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