Boundedness Of Fourier Integral Operator And Of Multilinear Commutators Of Marcinkiewicz Integral Operator

In this thesis, we investigate the boundedness of Fourier integral operatorand multilinear commutators of Marcinkiewicz integral operator with smoothfunction. It is composed of four chapters as the following.In chapter 1, we simply introduce the background and history of Fourierintegral operator and Marcinkiewicz integral operator . The current situations inthe field are generalized too.In chapter 2,we discuss the boundedness of Fourier integral operator. In thischapter, we prove that the operator is bounded from H^p to L^p and from H^p toL^q.In chapter 3, we consider the boundedness of multilinear commutators ofMarcinkiewicz integral operator related to Lipschitz functions. We obtain theproperties of the commutators on Hardy spaces.In chapter 4, we study the boundedness of the commutators furthermore.We show that the commutators is bounded from H (K|˙)_q1^{α, p} to (K|˙)_q2^{α, p}.