A Family Of Function Spaces And Composition Operators On Them

In the first chapter of this paper, we study the inclusion relations between different spaces F(p, g, s) which are the weighted Dirichlet-type spaces D when s = 0. In the second chapter we study the properties of the weighted Dirichlet-type spaces and composition operators on them. We not only characterize these spaces by Taylor series, but also give sufficient and necessary conditions in terms of Carleson measure for the boundedness and compactness of composition operator. Moreover, we apply the comparability propositions which induced from above sufficient and necessary conditions to discuss the relationships between the compactness of composition operator Cv and angular derivative or innerness of the inducing function , and so on.