Cesàro And Composition Operators On Holomorphic Function Spaces Of C~n

This paper is devoted to Ceshro operators and composition operators on holomorphic function spaces of Cⁿ.It consists of four chapters.In Chapter 1,the background and present conditions are introduced and summarized for the study of boundedness and compactness of Cesàro operators and composition operators,and we line the main results of the paper as follows.In Chapter 2,let g₁,g₂ be normal functions.For all 0＜p,q＜∞,the necessary and sufficient conditions are given for the Cesàro operator T_ψ:A_g1^p→A_g2^q being bounded or compact on Bergman type spaces.In Chapter 3,the boundness and compactness of Cesàro operator T_g from F(q) space to Bloch type space on the unit ball of Cⁿ for q＞-n-1,α＞0 are studied and the necessary and sufficient conditions are given for the Ceshro operator T_g.In Chapter 4,the equivalences of some compactness conditions for composition opreator between Bloch spaces on the polydisc of Cⁿ are studied.At the same time, the best simple expressions are obtained.