2011/09/30 by Anna Kamińska, Damian Kubiak · 1 citation
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces #Ball (mathematics) #Combinatorics #Computer science #Convex function #Dual (grammatical number) #Dual function #Dual representation #Dual space #Function (biology) #Function space #Functional analysis #Geometry #Interpolation space #Mathematical analysis #Mathematics #Pure mathematics #Reflexive space #Regular polygon #Space (punctuation) #Unit sphere #math.FA #msc:46B20 #msc:46B22 #msc:46B42 #msc:46E30
paper · pdf · doi:10.1016/j.na.2011.11.019
published as Nonlinear Anal. 75 (5) (2012), 2760-2773 · 16 pages
arxiv created 2011/12/13 · openalex publication_date 2011/12/16 · arxiv updated 2015/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The goal of this paper is to present an isometric representation of the dual space to Cesàro function space Cp,w, 1<p<∞, induced by arbitrary positive weight function w on interval (0,l) where 0<l\leqslant∞. For this purpose given a strictly decreasing nonnegative function Ψ on (0,l), the notion of essential Ψ-concave majorant f of a measurable function f is introduced and investigated. As applications it is shown that every slice of the unit ball of the Cesàro function space has diameter 2. Consequently Cesàro function spaces do not have the Radon-Nikodym property, are not locally uniformly convex and they are not dual spaces.