B-maximal commutators and commutators of Riesz-Bessel transforms on Morrey spaces

This thesis consists of three chapters. In the first chapter, definitions and properties of Lebesgue and Morrey spaces are presented, along with some concepts, notations, and theorems related to operators such as the maximal operator and the classical Riesz transform. In addition, the generalized translation operator associated with the Laplace-Bessel differential operator, which forms the basis of the thesis, and its properties are also presented. The boundedness theorems of the B-maximal operator, obtained via this operator, and the Riesz-Bessel transforms more general form of the classical Riesz transforms in Lebesgue and Morrey spaces are presented without proof. In the second chapter, the boundedness of the B-maximal operator and its commutator in the B-Morrey space is presented. In the final chapter, the strong and weak type boundedness of the Riesz-Bessel transform related to the generalized translation operator in B-Morrey space is examined. Additionally, the strong and weak type estimates of the commutator of the Riesz-Bessel transform and R_j^((k))in this space have been obtained.