Carleson Measures Supported On (-1,1) And The Related Hankel Matrices

Letμbe a finite positive Borel measure on D supported on (-1,1), p>0. We study the relationship between p-Carleson measureμand the elements of the related Hankel matrix. Moreover, whenμis supported on (-1,0) or (0,1), p≥1, we characterize p-Carleson measureμin terms of the operators induced by the related Hankel matrix. The thesis consists of the following three parts.The first part is concerned in giving the backgrouds of some function spaces. The importance of Carleson measure in functon spaces and operator theory is recited; the knowledge of the Hankel matrix and the main resultes of this thesis are also listed.In the second part, we study the relationship between p-Carleson mea-sures and the related Hankel matrices. We give and prove the main resultes of the thesis. At the same time, we explain that the main resultes are best by examples.Finally, we study the generalized Hilbert operators on the Dirichlet-type spaces.