A note on boundedness of operators in grand grand morrey spaces

Abstract

In this note we introduce grand grand Morrey spaces, in the spirit of the grand Lebesgue spaces.We prove a kind of reduction lemma which is applicable to a variety of operators to reduce their boundedness in grand grand Morrey spaces to the corresponding boundedness in Morrey spaces. As a result of this application, we obtain the boundedness of the Hardy-Littlewood maximal operator and Calder´on-Zygmund operators in the framework of grand grand Morrey spaces.