The boundedness of generalized fractional integral operators on some function spaces

This thesis is consists of four chapters. The fi rst chapter is devoted to the introduction. In the second chapter, some basic de finitions and theorems related to this study are given. In the third chapter, Lebesgue spaces, Morrey spaces, generalized Morrey spaces and generalized Campanato spaces are introduced and their fundamental properties are given. In the fourth chapter, fundamental properties of Riesz potential and generalized fractional integral operators are given and the boundedness of these operators in Lp Lebesgue spaces are investigated. The criteria for the boundedness of generalized fractional integral operators on Morrey spaces and generalized Morrey spaces is also given. Moreover, we also investigated the boundedness of the modifi ed generalized fractional integral operators in generalized Campanato spaces.