Dual spaces to Orlicz-Lorentz spaces

• Autorzy: Anna Kamińska , Karol Leśnik , Yves Raynaud
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 42B25: Maximal functions, Littlewood-Paley theory
• 46B10: Duality and reflexivity

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2014
• Tom: 222
• Numer: 3
• Strony: 229-261

Daty

wydano

2014

Twórcy

autor

Anna Kamińska

• Department of Mathematics, University of Memphis, Memphis, TN 38152, U.S.A.

autor

Karol Leśnik

• Institute of Mathematics, Faculty of Electrical Engineering, Poznań University of Technology, Piotrowo 3a, 60-965 Poznań, Poland

autor

Yves Raynaud

• Institut de Mathématiques de Jussieu, Université Paris 06-UPMC and CNRS, 4 place Jussieu, F-75252 Paris Cedex 05, France

Identyfikatory

DOI

10.4064/sm222-3-3