Study On Weighted Compound Operators In Analytic Function Space

In this paper,By means of the techniques of complex analysis and harmonic analysis,describes the boundedness,compactness and the essential norm of the weighted composition operators from the Bloch-type space to the log-Bloch space,and log-Bloch-type space,and from BMOA to the Zygmund space.In the first chapter,we introduce the development of the function space and the operator's theory.And the main contents of this paper are briefly described.In the second chapter,we introduce the definition of the function space concept and the weighted composite operator on several kinds of unit disks.In the third chapter,we depict the boundedness feature of the weighted composition operators from Bloch-type space to the log-Bloch space,and the Bloch-type space and from BMOA space to Zygmund space by means of complex analysis and harmonic analysis.The fourth chapter,we describes the compactness and the essential norm of the weighted composition operators from Bloch-type space to the log-Bloch space,and the Bloch-type space.The fifth chapter,we summarizes the conclusion and follow-up work in this paper.