Composition Operators From Bergman Space To Weighted Hardy Spaces

In this paper we mainly study the relations between the weighted Hardy spacesⅡ2(β) and the weight sequence{β(n)}, the composition operator and the weight se-quence{β(n)}. Despite both the disk algebra and a class of small weighted Hardy spaces are small, we still find the functions that are in A(D) but not in H2(β). Furtherly we discuss the composition operator from Bergman space into weighted Hardy spaces, and give a sufficient condition for the operator to be bounded and compact.In the first chapter, we discuss some related research background, and give some basic concepts and notions.In the second chapter, we introduce some basic definitions and properties of the weighted Hardy spaces, in particular, Bergman space.In the third chapter, we study the relations between the weighted Hardy spacesⅡ2(β) and the weight sequence{β(n)}, and some properties of the composition op-erator and the weight sequence{β(n)}. Despite both the disk algebra A(D) and the weighted Hardy spaces H2(β) with condition (?)1/3(n)2<+∞are "small", we still find the functions that are in A(D) but not in H2(β).In the fourth chapter, we discuss the composition operator from Bergamn space to weighted Hardy spaces, and give a sufficient condition for the operator to be bounded and compact.