Norm Attaining Operators On Analytic Function Spaces

Let D be the unit disc of complex plane and (?) be a holomorphic mapping from D to itself. Denote H(D) the space of all analytic functions on D. Then (?) induces a composition operator C(?):fâ†'fo(?). For any g∈H(D), it can induce an integral operator In this thesis, Norm-attaining composition operators and Norm-attaining inte-gral operators are investigated. There are three parts in this thesis as following.The first chapter is concerned in definitions and backgrounds of some clas-sical function spaces and norm-attaining operators. Some relative results are also listed.Chapter 2 is aimed at investigating the composition operators from Bαto Bβ. The norm of C(?) is estimated. We are also give necessary and sufficient conditions for norm-attaining composition operator C(?).In chapter 3, we study the integral operator Ig on the Bloch space, Dirichlet space and BMOA space. We give some conditions for integral operators to be norm-attaining.