The maximal operators associated with ∆B operators in Orlicz spaces

Our study is related to the singular integral operators, Orlicz spaces, which are important in harmonic analysis, and the boundedness of maximal operators connected to generalized shift operator. Firstly, in the introduction part, information will be given about the researchers who have papers concerned with thesis study and information about the goal of our thesis will be given. The second chapter contains some main concepts, theorems which will be apply to succeeding chapters. By giving the information about Orlicz spaces and Young's functions, which contain a significant part of our study, then Orlicz spaces are investigated briefly in third chapter. In the final chapter, the maximal integral operators which are important in our thesis of the problems of the boundedness of singular integral operators are investigated and the some results associated with the boundedness of Bmaximal operators connected to the generalized displacement operator in Orlicz spaces are given. Keywords: Generalized Shift operators, Laplace Bessel operator, Lebesgue space, Maximal operator, Maximal operator related to Laplace Bessel operator, Orlicz space