The boundedness of weighted hardy-littlewood maximal and riesz potential operators in variable exponent morrey spaces

In this study the boundedness of the weighted Hardy-Littlewood maximal and Riesz operators in the variable exponent Morrey spaces are proved.This thesis consists of five chapters.The first chapter is an introduction to the theory of the variable exponent Lebesgue and Morrey spaces. Moreover, it gives the origin of the theory and lists the relevant works of the various authors in choronological order.In the second chapter, we give the basic definitions and theorems of the theory.In the third chapter, the theory of the variable exponent Lebesgue and weighted variable exponent Lebesgue spaces and some important results related to the thesis are given.In the fourth chapter, the theory of the clasicall Morrey and the variable exponent Morrey spaces and the necessary conditions of the boundednes of the Hardy-Littlewood maximal and Riesz operators are given.In the last chapter, the definition of the weighted variable exponent Morrey spaces is given and the boundedness of the weighted Hardy-Littlewod maximal and weigheted Riesz operators on a bounded open domain is obtained.