On the behavior of some classical operators in vanishing Orlicz-Morrey spaces

In this study, a new type of vanishing Orlicz-Morrey space has been introduced and the boundedness of classical operators of harmonic analysis and their commutators in these spaces have been investigated. In the first part of this study, which consists of five parts, some basic information about many mathematicians who have researched on this subject matter in the literature is given and the purpose of this study is mentioned. In the second part, general information and some basic definitions about the basic concepts, spaces and operators related to our work are given. In the third chapter, the definition of Orlicz-Morrey spaces is given and some classical and new vanishing conditions that define certain closed subspaces of these spaces are introduced. In the fourth chapter, the boundedness properties of maximal, singular and potential operators on the new vanishing Orlicz-Morrey spaces that were introduced in the third chapter are investigated. In the fifth chapter, which is the last part of this thesis, the analysis in the fourth chapter is made for the commutators of these classical operators.