Spanne-Guliyev and Adams-Guliyev type results for the boundedness of the Riesz potential

In this master thesis, information about the results of the Riesz potentials and boundedness of Riesz potentials will be given. This thesis consists of four chapters. The first section is devoted to the introduction. In the second section, some basic concepts, notations and theorems that will come in handy in the following sections are included. Morrey spaces, Generalized Morrey spaces and the definition and properties of the Hardy-Littlewood maximal operator are given, also the results that related to the boundedness of the Hardy-Littlewood maximal operator on the Lp(Rn),Mp,λ(Rn) and Mp,ϕ(Rn) spaces are included. In the third section, Riesz potential in the classical Lebesgue spaces will be defined, and their existence and boundedness properties are investigated. In the last section, by using the expressions that obtained by Guliyev [5, 11, 12, 13], Spanne-Guliyev and Adams-Guliyev type of results for the boundedness of the Riesz potential operator in Generalized Morrey spaces are included.