Dual spaces to Orlicz-Lorentz spaces

Anna Kamińska, Karol Leśnik, and Yves Raynaud. "Dual spaces to Orlicz-Lorentz spaces." Studia Mathematica 222.3 (2014): 229-261. <http://eudml.org/doc/286639>.

@article{AnnaKamińska2014,
abstract = {For an Orlicz function φ and a decreasing weight w, two intrinsic exact descriptions are presented for the norm in the Köthe dual of the Orlicz-Lorentz function space $Λ_\{φ,w\}$ or the sequence space $λ_\{φ,w\}$, equipped with either the Luxemburg or Amemiya norms. The first description is via the modular $inf\{∫ φ⁎(f*/|g|)|g|: g ≺ w\}$, where f* is the decreasing rearrangement of f, ≺ denotes submajorization, and φ⁎ is the complementary function to φ. The second description is in terms of the modular $∫_\{I\} φ⁎((f*)⁰/w)w$,where (f*)⁰ is Halperin’s level function of f* with respect to w. That these two descriptions are equivalent results from the identity $inf\{ ∫ ψ(f*/|g|)|g|: g ≺ w\} = ∫_\{I\} ψ((f*)⁰/w)w$, valid for any measurable function f and any Orlicz function ψ. An analogous identity and dual representations are also presented for sequence spaces.},
author = {Anna Kamińska, Karol Leśnik, Yves Raynaud},
journal = {Studia Mathematica},
keywords = {Orlicz-Lorentz spaces; Lorentz spaces; dual spaces; level function; Calderón-Lozanovskii spaces; r.i. spaces},
language = {eng},
number = {3},
pages = {229-261},
title = {Dual spaces to Orlicz-Lorentz spaces},
url = {http://eudml.org/doc/286639},
volume = {222},
year = {2014},
}

TY - JOUR
AU - Anna Kamińska
AU - Karol Leśnik
AU - Yves Raynaud
TI - Dual spaces to Orlicz-Lorentz spaces
JO - Studia Mathematica
PY - 2014
VL - 222
IS - 3
SP - 229
EP - 261
AB - For an Orlicz function φ and a decreasing weight w, two intrinsic exact descriptions are presented for the norm in the Köthe dual of the Orlicz-Lorentz function space $Λ_{φ,w}$ or the sequence space $λ_{φ,w}$, equipped with either the Luxemburg or Amemiya norms. The first description is via the modular $inf{∫ φ⁎(f*/|g|)|g|: g ≺ w}$, where f* is the decreasing rearrangement of f, ≺ denotes submajorization, and φ⁎ is the complementary function to φ. The second description is in terms of the modular $∫_{I} φ⁎((f*)⁰/w)w$,where (f*)⁰ is Halperin’s level function of f* with respect to w. That these two descriptions are equivalent results from the identity $inf{ ∫ ψ(f*/|g|)|g|: g ≺ w} = ∫_{I} ψ((f*)⁰/w)w$, valid for any measurable function f and any Orlicz function ψ. An analogous identity and dual representations are also presented for sequence spaces.
LA - eng
KW - Orlicz-Lorentz spaces; Lorentz spaces; dual spaces; level function; Calderón-Lozanovskii spaces; r.i. spaces
UR - http://eudml.org/doc/286639
ER -