New examples of K-monotone weighted Banach couples

• Autorzy: Sergey V. Astashkin , Lech Maligranda , Konstantin E. Tikhomirov
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 46B70: Interpolation between normed linear spaces
• 46B42: Banach lattices

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2013
• Tom: 218
• Numer: 1
• Strony: 55-88

Daty

wydano

2013

Twórcy

autor

Sergey V. Astashkin

• Department of Mathematics and Mechanics, Samara State University, Acad. Pavlova 1, 443011 Samara, Russia

autor

Lech Maligranda

• Department of Engineering Sciences and Mathematics, Luleå University of Technology, SE-971 87 Luleå, Sweden

autor

Konstantin E. Tikhomirov

• Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G2G1, Canada

Identyfikatory

DOI

10.4064/sm218-1-4