Boundedness Of Fourier Integral Operator On Herz Spaces

In this paper, we study the boundedness of Fourier integral operators onmany kind of Herz spaces and Hardy spaces associated with Herz spaces. Also,we study the commutators of multiplier operators, which contains the modelcase of Fourier integral operators, with the Lipschitz functions. This paper isorganized as as follows.In chapter 1, we simply introduce the development in the study of the bound-edness of Fourier integral operators and the commutators of some operators withsmooth functions.In chapter 2, we study the boundedness of Fourier integral operators onthree kind of Herz spaces and Hardy spaces associated with Herz spaces. Wedecompose the kernel of Fourier integral operators in the frequency domain bytwice Littlewood-Paley decomposition, and find the relation between the singulardomain of Fourier integral operators and the standard circular by Taylor seriesexpansion, and then get the integral estimate of kernel on the standard circularusing the pointwise estimate of kernel. Finally, we obtain the main results of thischapter.In chapter 3, we investigate the boundedness of Fourier integral operatorson the special Herz spaces. Since the conditions required in the boundedness ofFourier integral operators from L~2 to L~p(2 < p <∞) and from L~p to L~2(1