The Properties Of Some Operators From Bloch Spaces To Q_k(p,q)Spaces

Operator theory in analytic function space is an important tool for studying classical problems in function theory.Since Nordgren gave sufficient conditions for composite operators to be bounded operators in Hardy space from the 20th century to the 60th century,operator theory has attracted great interest of many scholars at home and abroad.After many years of research and development,it has become a leading field.Domain has made a lot of profound research results,and gradually formed a relatively complete theoretical system.In this paper,we mainly study the properties of weighted composite operators from generalized weighted Bloch space to QK(p,q)space on unit disk,and further discuss the Riemann-Stieltjes operators of Blog? space and QK(p,q)space.This article consists of five chapters as follows:In the first chapter,the historical background of the formation of analytic function space and operator theory is summarized.The development history,research purpose and significance are briefly described.The research status and some existing conclusions of operator theory on Bloch type space and QK(p,q)type space are also presented.In the second chapter,we introduces the basic knowledge of QK(p,q)space,Bloch type space,Riemann-Stieltjes operator and weighted composition operator,and intro-duces some symbols and lemmas.In the third chapter,we discussed the weighted composition operator uC?:Blog??QK(P,q)space.The theorems of uC?:Blog??QK(p,q)as bounded operator and compact operator are obtained.In the fourth chapter,we discuss the boundedness of Riemann-Stieltjes operators of Blog? space and QK(p,q)space.In the fifth chapter,we summarize the conclusions obtained in this paper and put forward some questions for further studies in this research field.