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 for some p ∈ [1,∞], then . 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm218-1-4,
author = {Sergey V. Astashkin and Lech Maligranda and Konstantin E. Tikhomirov},
title = {New examples of K-monotone weighted Banach couples},
journal = {Studia Mathematica},
volume = {215},
year = {2013},
pages = {55-88},
zbl = {1292.46013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm218-1-4}
}
Sergey V. Astashkin; Lech Maligranda; Konstantin E. Tikhomirov. New examples of K-monotone weighted Banach couples. Studia Mathematica, Tome 215 (2013) pp. 55-88. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm218-1-4/