New examples of K-monotone weighted Banach couples

Sergey V. Astashkin, Lech Maligranda, and Konstantin E. Tikhomirov. "New examples of K-monotone weighted Banach couples." Studia Mathematica 218.1 (2013): 55-88. <http://eudml.org/doc/285410>.

@article{SergeyV2013,
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 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 ∈ [1,∞], 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.},
author = {Sergey V. Astashkin, Lech Maligranda, Konstantin E. Tikhomirov},
journal = {Studia Mathematica},
keywords = {-functional; -method of interpolation; -monotone couples; -decomposable Banach lattices; symmetric spaces; ultrasymmetric spaces; weighted symmetric spaces; Lorentz spaces; Marcinkiewicz spaces; Orlicz spaces; regularly varying functions},
language = {eng},
number = {1},
pages = {55-88},
title = {New examples of K-monotone weighted Banach couples},
url = {http://eudml.org/doc/285410},
volume = {218},
year = {2013},
}

TY - JOUR
AU - Sergey V. Astashkin
AU - Lech Maligranda
AU - Konstantin E. Tikhomirov
TI - New examples of K-monotone weighted Banach couples
JO - Studia Mathematica
PY - 2013
VL - 218
IS - 1
SP - 55
EP - 88
AB - 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 $t^{1/p}$ for some p ∈ [1,∞], 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.
LA - eng
KW - -functional; -method of interpolation; -monotone couples; -decomposable Banach lattices; symmetric spaces; ultrasymmetric spaces; weighted symmetric spaces; Lorentz spaces; Marcinkiewicz spaces; Orlicz spaces; regularly varying functions
UR - http://eudml.org/doc/285410
ER -