Boundedness of the integral operators of the harmonic analysis in generalized Morrey spaces

In this master thesis, information about the generalized Morrey spaces and the boundedness of integral operators of harmonic analysis in these spaces will be given. This thesis consists of three chapters. The first chapter is devoted to the introduction. In the second chapter, some basic concepts, notations and theorems about the operators, definitions and properties of the Lebesgue spaces, Morrey space, Generalized Morrey space that is closely related to the topics that will be explored in the next section are included. Also the theorems about the boundedness of the maximal operator, singular integral operator, Riesz potentials in the Lp(Rn) Lebesgue spaces are given without proof. In the third chapter, the boundedness of Hardy-Littlewood maximal operator in the Mp,ϕ(Rn) spaces is shown with the help of the Gulyev's lokal inequalities which was given by Guliyev [11]. The boundedness of Iα Riesz potential from the space Mp,ϕ(Rn) to Mq,ϕ(Rn) is shown as Spanne and Adams type boundedness with two different ways. For this aim two different theorems which were given by Guliyev [11] are used. Finally, the boundedness conditions are given for T Calderon-Zygmund singular integral operator in the Mp,ϕ(Rn) spaces. Keywords: Lp spaces, Morrey spaces, Generalized Morrey spaces, maximal operator, singular integral operator, Riesz potential.