2018/08/05 by Al Azhary Masta, Siti Fatimah, Masta, Al Azhary +3
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Mathematical Approximation and Integration #math.FA #msc:42B35 #msc:46B25 #msc:46E30
paper · pdf · doi:10.48550/arxiv.1808.01698
arxiv created 2018/08/05 · arxiv updated 2018/08/07
Orlicz--Morrey spaces are generalizations of Orlicz spaces and Morrey spaces which were first introduced by Nakai. There are three versions of Orlicz--Morrey spaces, i.e: Nakai's (2004), Sawano--Sugano--Tanaka's (2012), and Deringoz--Guliyev--Samko's (2014) versions. On this article we will discuss the third version of weak Orlicz--Morrey space which is seen as an enlargement of third version of (strong) Orlicz--Morrey space. Similar to its first version and second version, the third version of weak Orlicz-Morrey space is considered as a generalization of weak Orlicz spaces, weak Morrey spaces, and generalized weak Morrey spaces. In this study, we will investigate some properties of the third version of weak Orlicz--Morrey spaces, especially the sufficient and necessary conditions for inclusion relations between two these spaces. One of the keys to get our result is to estimate the quasi-norm of characteristics function of open balls in ℝn.