A Class Of New Operators On Function Spaces

This thesis studies the boundedness and compactness of the differentiation com-position operator from the ZgmundBloch space to the Bloch. space and the weighted composition operator from the Berslog a,q space to Berslogβ,q space. There are four parts in this paper.In part1We introduce the related research background and research status and state the main results of this paper.In part2We give and prove the necessary and conditions of differentiation compo-sition operator is a bounded or a compact operator from the ZgmundBloch space to the Bloch space.In part3We give and prove the necessary and conditions of weighted composition operator is a bounded or a compact operator from the Bersloga,q space to the Berslogβ,q space.In part4Summary and outlook.