General singular integrals and L^p boundedness conditions

This thesis consists of four chapters. In first chapter, we gave introduction. The second chapter some basic information and theorems are given which will be used in following chapters.İn the third chapter is devoted to the calderon?zygmund decomposition, general singular integrals, the implication of the L^p boundedness implies weak type (1,1) boundedness, discussion on maximal singular integrals and then boundedness for maximal singular integrals implies weak type (1,1) boundedness .Finally, we consider sufficient conditions for L^p boundedness of singular integrals, an example, necessity of the cancellation condition and sufficient conditions for L^p boundedness of maximal singular integrals.