Boundedness of projected composition operators over the unit disc

In the present paper, we carry forward R. Rochberg's work [4] on the boundedness of composition operators associated to continuous symbols of norm greater than 1. More general sufficient conditions and necessary conditions are given for the boundedness of Kφ:=PH2Dφ where Dφ:C[z]→L2(T) is the composition operator of the symbol φ.