A New Characterization Of Boundedness And Compactness For The Generaliazed Composition Operators And Their Differences

In this paper,we give some new characterizations of the boundedness and compactness for the integral composition operators and the differences of differ-entiation composition operators on spaces of analytic functionsWe divide this article into five chaptersIn the first chapter,we briefly introduce the research background and cur-rent situation of the composition operators,integral composition operators and differention composition operators and give the main conclusion of this thesisIn the second chapter,we give some basic knowledge about integral compo-sition operators,differention composition operators and their differences,bound-edness,essential norm,compactness and some spaces of analytic functionsIn the third chapter,we characterize the boundedness and compactness for the integral composition operators on the Bloch type space in a new wayIn the fourth chapter,we give a characterization of the the boundedness and compactness for the differences of differentiation composition operators on the Bloch space.The last chapter,we present the summary and outlook of this paperThe innovation of this paper is mainly reflected in two aspects:first,the con-struction of test functions used in the process of proof is new;Secondly,we char-acterize the boundedness and compactness for the integral composition operators and the differences of differentiation composition operators in a more convenient way by computing the Taylor expanded form of the test functions,so as to make the conclusion more perfect.