On the singular integral operators with rough kernel

This thesis consist of three chapters. In first chapter we gave some basic information and theorems which will use in third chapter.The second chapter is devoted to the teory of the Hardy-Littlewood maximal operator as the basis of singular integral operators. It also include Calder?n-Zygmund decomposition which is extremely useful in harmonic analysis, Marcinkiewicz interpolation theorem and the teory of the A_p weights.Finally, in third chapter we consider the L^p boundedness and the weighted L^p boundedness of singular integral operators with rough kernel.Key Words: A_p weights, Calder?n-Zygmund decomposition, Hardy Littlewood maximal operator, Marcinkiewicz interpolation theorem, Singular integral operator with rough kernel .