Toeplitz Operator And Composition Operator On Analytic Function Space Of Several Complex Variables

In the first chapter, we study a sufficent condition for a operator is compact on Bergman space of the unit ball. With a additional condition, we obtain the sufficent condition for a operator is compact. The situation of Bergman space in the disk is obtained by Miao Jie and Zheng Dechao.In the second chapter, we use the tools of Carleson measure, charactering Toeplitz opeartor and compositon operator on Bergman space of bounded symmetric domains. We study the relation of Carleson measure and Toeplitz operator on Bergman space of bounded symmetry domians, and give a charactering of a composition operator, also give a charactering of bounded and compact weighted composition operator.In the third chapter, we use the tool of Carleson measure, charactering the bounded and compact of weighted composition operator on Bergman space on strongly pseudoconvex domains, these results generalized the results of G.Mirzakarimi and K.Seddighi.In the fourth chapter, we use reproducing kernel and Carleson measure charactering pointwise multipliers between the Hardy space and Bergman space, Bergman space and Bergman space on the unit ball.In the fifth chapter, we use the the methods of function theoryestablised a class of analytic reproducing kernel space, we call it a generalized Arveson space.We study the relationship of these space, and obtain some intersting results, we also defined Toeplitz C*-algebra on the generalized Areveson space, obtain some results of Toeplitz C*-algebra on the generalized Areveson space.In the six chapter, we use the methods of reproducing kernel and Carleson measure charactering the pointwise multipliers on the Hardy space, Bergman space on the polydiscs, we also obtain a necessary condition for a composition operator to be a compact operator, and a addition result on the range of composition operator on the Hardy space.