Composition Operators On Several Classes Of Holomorphic Function Spaces Between The Discussion Of Child Nature

In the paper,we will study the property of the composition operator acting different holomorphic function spaces as follow.1.The property of the composition operator C_φfrom Hardy space to weighted Hardy space on the unit disc.Wu shuhong^[3] got the condition for C_φfrom Hardy space to weighted Hardy space to be bounded and obtained the sufficient conditions for C_φto be compacted, but he did not give the necessary conditions of the compact composition operator.In the paper,Chapter two describes the equivalent norm of weighted Hardy space.By using it, we obtain the sufficient and necessary conditions for C_φto be bounded or compacted operators from Hardy space to weighted Hardy space.2.The property of the composition operator C_φfrom weighted Bergman space to q -Bloch space on the unit polydisc Dⁿ.In 2006,Tang xiaomin and Hu zhangjian studied the characterization of the composition operator between weighted Bergman space and q-Bloch space on the unit disc.As the generalization of composition operator in the domain,In the paper Chapter three discusses the boundedness and compactness of the composition operator C_φ, which acts between weighted Bergman space and q-Bloch space on the unit polydisc Dⁿ.we give the sufficient conditions for C_φto be bounded or compacted operators from weighted Bergman space to q-Bloch space.