In this paper, we introduce the generalized grand Morrey spaces in the framework of probability space setting in the spirit of the martingale theory and grand Morrey spaces. The Doob maximal inequalities on the generalized grand Morrey spaces are provided. Moreover, we present the boundedness of fractional integral operators for regular martingales in this new framework.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.