Two weighted inequalities for maximal and singular integral operators in global morrey type spaces

This thesis consists of six chapters. The first chapter is devoted to the introduction. In the second chapter, basic definitions and theorems are given. In addition, Morrey spaces, local Morrey spaces and generalized Morrey spaces are recalled and some basic properties of these spaces are mentioned. In the third part of the thesis, weighted global Morrey type spaces are reminded and in the first part of this part, two weighted boundedness of maximal operators in weighted global Morrey type spaces is proved. In the second part of this chapter, the two-weight boundedness of maximal commutators in weighted global Morrey type spaces is discussed. The fourth part of the thesis deals with the two-weight boundedness of singular operators and singular commutators in weighted global Morrey type spaces. In the first part of this chapter, two-weight inequalities of singular operators in weighted global Morrey type spaces are analyzed and the proof of the theorem giving the necessary condition for two-weight boundedness is shown. In the second part of this chapter, two-weight boundedness of singular commutators in weighted global Morrey type spaces is proved. In the fifth part of the thesis, the application of some inequalities in weighted global Morrey type spaces using the results obtained in the other chapters is given. In the last part of the thesis, the results obtained are analyzed.