Difference Of The Products Of Volterra Type And Composition Operators

Operator theory in function spaces becomes a hot issue of research. As the carrier of research is function spaces, the common operator must be derived from certain function, so we need to discuss the relation between. In this paper, we characterize the difference of the products of the integral type and composition operators acting from the bounded function space to the Bloch space in the disk, and necessary and sufficient conditions are given for the difference to be bounded and compact.The paper is mainly divided into five chapters.The first chapter is the introduction of the whole paper. We talk about the back-ground of this paper, and make plans for the research of the problem.Next chapter of the paper, some important concepts and lemmas which are related to the article are given. They are the foundations and tools of the later work, and we will use them without proof.The third chapter discusses the properties of the product operators, using the lemma and conclusions, the equivalent conditions of boundedness and compactness of operators are given.The fourth chapter,similar with the third, discuss another type of product opera-tors.At last, we summarize the work of the whole paper and give some open problems about the problem.