Stevic-Sharma Operator From Zygmund-type Spaces To Bloch-Orlicz Spaces

The operator theory in function spaces is one of the important research fields of function theory,in this paper,by using analysis methods and constructing test functions,the boundedness and compactness of the Stevic-Sharma operator and the Volterra-type operators which from the Zygmund-type spaces to the Bloch-Orlicz spaces are researched.The concrete contents of this paper are as follows:The first chapter is the introduction,in the first place,we introduce the research background and current situations of the Zygmund-type spaces and the Bloch-Orlicz spaces,as well as the relevant theoretical knowledge,especially the knowledge of the Bloch-Orlicz spaces,and then we introduce a number of lemmas which the article needs to be used during the prove of theorem,finally,the main results of this paper are givenIn the second chapter,the boundedness and compactness of Stevic-Sharma operator from the Zygmund-type spaces to the Bloch-Orlicz spaces are studied,and the neces-sary and sufficient conditions of the boundedness and compactness of the Stevic-Shama operator from the Zygmund-type spaces to the Bloch-Orlicz spaces are obtained.In the third chapter,the boundedness and compactness of Volterra-type operators from the Zygmund-type spaces to the Bloch-Orlicz spaces are studied,then the equivalent conditions of the boundedness and compactness of the Volterra-type operators from the Zygmund-type spaces to the the Bloch-Orlicz spaces are also obtained.