Third Version of Weak Orliczâ€“Morrey Spaces and Its In-clusion Properties - Masta, Al Azhary; Fatimah, Siti; Taqiyuddin, Muhammad (Universitas Pendidikan Indonesia, 2019)
Orliczâ€“Morrey spaces are generalizations of Orlicz spaces and Morrey spaces which were first introduced by Nakai. There areÂ threeÂ versionsÂ ofÂ Orliczâ€“MorreyÂ spaces.Â InÂ thisÂ article,Â we discussedÂ theÂ thirdÂ versionÂ ofÂ weakÂ Orliczâ€“MorreyÂ space, which is an enlargement of third version of (strong) Orliczâ€“ Morrey space. Similar to its first version and second version, the third version of weak Orlicz-Morrey space is considered asÂ aÂ generalizationÂ ofÂ weakÂ OrliczÂ spaces,Â weakÂ Morrey spaces,Â andÂ generalizedÂ weakÂ MorreyÂ spaces.Â ThisÂ study investigatedÂ someÂ propertiesÂ of the thirdÂ version of weak Orliczâ€“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 â„.