The Properties Of Volterra Type Composition Operators On Analytic Function Spaces

With the development of fluid mechanics,dynamic systems and information control,and analytic function space theory and operator theory have been widely used in various fields as reasearch tools.People's research on single complex transformation theory sys-tem has become more and more complete.However,for multiple complex,there are still many problems that need to be solved.This paper is mainly based on the F(p,q,s)space on the unit ball.Discussion on some properties of Volterra type composite operators.The main content of the full text has six chapters:In the first chapter,this paper introduces some research backgrounds,research signif-icance and research status of single complex and multiple complex and composite opera-tors,as well as the research status and existing results of the essential norm in the analytic function space on the unit ball.In the second chapter,we mainly introduce the basic knowledge of F(p,q,s)space,Bloch space and ?-Zygmund space.At the same time,some lemmas are given to prepare for the later research.In the third chapter,through the selection of the test function in F(p,q,s)space and application of the previous research results,the article discuss the boundedness and the estimation of Volterra-type composition operator on F(p,q,s)space on unit ball.In the fourth chapter,it mainly uses the test function to complete the boundedness and the essential norm estimation of the logarithm Bloch space to the F(p,q,s)space Volterra type composition operator on the unit ball,and obtain corresponding in conclusion.In the fifth chapter,according to the limitation of ?,we discuss the boundedness of the Volterra-type composite operator from ?-Zygmund space on the unit sphere to F(p,q,s)space and its intrinsic norm,and get the conclusions.In the sixth chapter,we summarize the research significance of the conclusions of this paper and the future prospects of this research field.