Third Version of Weak Orliczâ€“Morrey Spaces and Its In-clusion Properties - Masta, Al Azhary; Fatimah, Siti; Taqiyuddin, Muhammad (Indonesian Journal of Science and Technology, 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„.