Extended Cesàro Operators On Holomorphic Function Spaces In C～n

This paper is devoted to the study of weighted Cesàro operators on holomorphic function spaces on C~n. It consists of the following four chapters.In Chapter 1, the background and present state are introduced and summarized for the study of boundedness and compactness of weighted Cesàro operators.In Chapter 2, the boundedness and compactness of the Extended Cesàro operators T_g between different Bloch-type spaces,little Bloch-type spaces and Bloch-type~* spaces are discussed on the polydisc, three necessary and sufficient conditions of the boundedness and compactness are obtained.In Chapter 3, two necessary and sufficient conditions are given for the Extended Cesàro operators to be bounded and compact fromβμspace toβνspace and fromβμ,οspace toβν,οspace on the unit ball of C~n.In Chapter 4,two necessary and sufficient conditions are given for the Extended Cesàro operators T_g to be bounded or compact from Dirichlet type spaces D_p toμ-Bloch spacesβμon the unit ball of C~n.