Multipliers On Analytic Function Spaces

The boundedness and the compactness of pointwise multipliers on some holomorphic function spaces in the unit disk D={z:|z|<1}of C and in the unit ball B_n={z(?)Cⁿ:|z|<1}of Cⁿare studied in this paper respectively.This paper include four chapters.On the one hand,we introdeced some research background and the development of function spaces;On the other hand,some definition of function spaces and some related results of Carleson measures are intro-duced in Chapter 1.The boundedness of multipliers from the random Dirichlet series on the Dirichlet spaces was characterized by Cochran.Liu and Hu general-ized Cochran's results.The boundedness of multipliers from random se-ries on Dirichlet spaces in the unit disc are showed by combining Cochran and Liu's results in Chapter 2.The boundedness and Compactness of multipliers on Bergman spaces in the unit ball of Cⁿare showed by combing Feldman and Zhao's results in Chapter 3.The conclusion of the thesis and some unsolved problems are given in Chapter 4.