Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774617 | Journal of Mathematical Analysis and Applications | 2017 | 19 Pages |
Abstract
The goal of this paper is to present a complete characterization of points of order continuity in abstract Cesà ro function spaces CX for X being a symmetric function space. Under some additional assumptions mentioned result takes the form (CX)a=C(Xa). We also find simple equivalent condition for this equality which in the case of I=[0,1] comes to Xâ Lâ. Furthermore, we prove that X is order continuous if and only if CX is, under assumption that the Cesà ro operator is bounded on X. This result is applied to particular spaces, namely: Cesà ro-Orlicz function spaces, Cesà ro-Lorentz function spaces and Cesà ro-Marcinkiewicz function spaces to get criteria for OC-points.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Tomasz Kiwerski, Jakub Tomaszewski,