Properties Of Composition Operators On Weighted Lipschitz Spaces

The research on the related properties of compound operator in analytic function space,boundedness and compactness are the main research areas.The discussion is dis-cussed in two different regions of analytic function space:the first one is the analytic function space on the unit disk in the one complex plane;the other is the resolution on the unit ball in C~n Function space.The multi-dimensional function space structure on the unit sphere is more compli-cated than the one-dimensional function space.Many basic properties of the space di-mension can not be guaranteed from one dimension to multi-dimension.Therefore,the corresponding research is also more difficult than the one on the unit disk.For example,any domain in the complex plane is a purely pure domain,but this property no longer holds true in multidimensional function space.There is also no Riemann mapping the-orem in multidimensional function space,which is similar to that in one-dimensional function space.Multidimensional function space The formation of the middle domain is also more complicated.The two most basic domains,hypersphere and multi-cylinder,are not purely equivalent,which all pose some challenges to the study of multiple changes.However,Study its meaning.In the Lipschitz space on the unit disc in a one-dimensional analytic function,the boundedness and compactness of the composite operator are obtained in the literature cite RH 2006.The multidimensional analytic function space In the Lipschitz space on the unit sphere of the unitary ball,the characterization of the boundedness and compactness of the weighted composite operator obtains the corresponding theorem in the literature cite DJ2012.In this paper,we introduce the related theorem of induced distance in space and discuss the related properties of weighted composite operator in C~n.This article mainly studies as follows:1.Characterize the boundedness and compactness of the complex operator Lipschitz space in C~n;2.Characterize the correlation between the weighted Lipschitz type space and the weighted Bloch type space in one-dimensional space.Through the discussion in this paper,we mainly obtain the relevant theorems on the boundedness and compactness of compound operators in the weighted Lipschitz space,further deepen the understanding of the compound operators in analytic function space,and to a large extent Enriched the conclusion about the equivalence between different analytic spaces.