Weighted Composition Operators On The Weighted Bergman Space

In this paper,we mainly study the basic problems of weighted composition operators, which are boundedness,compactness,essential norm and norm etc,on the Bergman spaces on the open unit disk and weighted Bergman spaces on the unit ball.In the first chapter,we discuss some related research ground of weighted composition operators,and show the research significance.In the second chapter,we study the basic properties of bounded and compact weighted composition operators on the Bergman spaces on the open unit disk and use the above properties to characterize the boundedness and compactness of composition operators on the Bergman space A²(G),which G is a simply connected domain.In the third chapter,we express the essential norm of a weighted composition operator on weighted Bergman spaces of the unit ball using boundary properties of weighted pull-back measure.In the fourth chapter,the sufficient and necessary conditions,which W_ψ,φ is a bounded or compact operator between H^∞(B_N) and weighted Bergman spaces A_α^p(B_N), can be obtained and meanwhile the norm is expressed.