Riesz-Bessel transformations obtained through generalized shift in weighted Lorentz space and the boundedness of some classical operators

This present thesis is consisted of five chapters. In the first chapter, it has been mentioned about the basic concepts and some theorems. In the second chapter, the generalized shift has been given. Moreover, it has been focused on the high order Riesz transformations obtained through generalized shift operator in the third chapter. Then, `Weighted Lorentz Spaces? and the boundedness of classical Riesz transformations on these spaces have been clarified in the fourth chapter. Finally, in the last chapter, the boundedness of some classical operators on the Weighted Lorentz Spaces have been analyzed. Keywords: Calderon Zygmund operator, Fractional Integral Operator, Generalized Shift Operator, Riesz transformations, Weighted Lorentz Spaces.