The Spanne and Adams types boundednesses of the generalized Riesz potential operator on the Morrey spaces

This thesis consists of five chapters. The first chapter is devoted to the introduction. In this section, the history of Morrey spaces and the generalized Riesz potential are given. In the second chapter, basic definitions, lemmas and theorems are given. In the third chapter, algebraic and topological structures of Morrey spaces are examined. In the fourth chapter, the boundedness of the Riesz potential in Morrey spaces is examined. In the fifth chapter, the Spanne and Adams type boundedness of the generalized Riesz potential in Morrey spaces are examined. Local inequalities are used in the proof of our theorems. Thanks to these local inequalities, it is done without the need for the monotonous feature of the functions we have used.