Higher order Riesz transforms related to Schrodinger type operators and their comutators in local generalized Morrey spaces

In this doctoral thesis, the boundedness of fractional maximal operators, higher order Riesz transformations and their commutators corresponding to Schrödinger type operators in some Morrey type spaces corresponding to Schrödinger type operators were investigated and original results were obtained. In the first chapter, the importance, scope and purpose of the research are expressed and information is given about the contributions of our study to science. In the second chapter, some basic definitions and characteristics of the thesis will be given. In the third chapter, brief information is given about the materials and methods related to the thesis topic. The fourth chapter consists of two parts. In the first part, the boundedness of the fractional maximal operator and its commutators corresponding to Schrödinger operator in generalized Morrey spaces and vanishing generalized Morrey spaces corresponding to Schrödinger operator are proved. In the second part, the boundedness of the higher order Riesz transformations and their commutator operators corresponding to the Schrödinger operator in local generalized Morrey spaces, generalized Morrey spaces and vanishing generalized Morrey spaces corresponding to the Schrödinger operator, respectively, are proved. The results obtained in the chapter are original. In the last chapter, the aims and objective of researching the thesis topic is briefly mentioned.