New examples of K-monotone weighted Banach couples

作者：Astashkin Sergey V^*; Maligranda Lech; Tikhomirov Konstantin E

来源：Studia Mathematica, 2013, 218(1): 55-88.

DOI：10.4064/sm218-1-4

• K-functional
• K-method of interpolation
• K-monotone couples
• w-decomposable Banach lattices
• symmetric spaces
• ultrasymmetric spaces
• weighted symmetric spaces
• Lorentz spaces
• Marcinkiewicz spaces
• Orlicz spaces
• regularly varying functions.

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 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 PIP for some p E [1, infinity], 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 find conditions which guarantee that (X, X (w)) is K-monotone.

• 出版日期2013