Carleson Measure And Some Operators On Analytic Function Spaces

In this paper, we study Carleson measures, the operators for spaces of Dirichlet type, products of Volterra-type operators and composition operators on logarithmic Bloch space, H∞loglog space and the connection between biharmonic Green function and Bergman kernel function. It is divided into six chapters. Specific content is as follows:In Chapter1, we briefly explains the historical background and development trends.In Chapter2, we study the boundedness of connection between Carleson mea-sure and Berezin transform. We characterize the Carleson measures by the perspec-tion of pseudo-hyperbolic metric, and discuss the relationship between s-logarithmic a-Carleson measures and its Berezin transfrom through the pseudo-hyperbolic met-ric. Finally, we obtain a result according to the relationship of them.In Chapter3, we study the connection between Jg and the Carleson measure on Dαp. Then it extend to the sufficient or necessary condition about the boundedness of Mg, Ig and Jg.In Chapter4, we characterize the boundedness and compactness of the prod-ucts of Volterra-type operators and composition operators on the logarithmic Bloch space LB and little logarithmic Bloch space LB0. Then we extend to the bounded-ness and compactness of Volterra-type operators and composition operators on the logarithmic Bloch space LB and little logarithmic Bloch space LB0.In Chapter5, we characterize some properties about H∞loglog space.In Chapter6, we study the connection between biharmonic Green function and Bergman kernel function.