Rudin’s Orthogonality And The Compactness Of Composition Operators On The Weighted Hardy Spaces

In this thesis, we study the compactness of composition operators Cφ on the weighted Hardy space H2(β), providing the necessarity and sufficiency of com-pact composition operator Cφ when φ satisfies the Rudin’s orthogonality condi-tion. Moreover, we provide a new characteration for the essential norm of the composition operator, and we give a completely characteration for Cφ under cer-tain conditions.In chapter1, we discuss some related research background, and we give some basic concepts and notations. At last, we show the significance of research work.In chapter2, we discuss the problem of Rudin’s orthogonality and the com-pactness of composition operators on the weighted Hardy spaces in detail.In chapter3, we discuss the problem of the Rudin’s orthogonality condition and the structure of composition operators Cφ, and we give a completely charac-teration for Cφ under certain conditions.