Characterizations Of Holomorphic Function Spaces And Related Operator Theory

This thesis gives some new characterizations of the Bloch spaces,theα-Bloch spaces,the Besov spaces,the weighted Bergman spaces,the Dirichlet type spaces and the Q_p spaces on the unit ball.The boundedness and compactness of Riemann-Stieltjes operators on the Hardy spaces,the weighted Bergman spaces, the mixed norm spaces,theα-Bloch spaces and the Zygmund type spaces are studied in this thesis.Charpter 1 is concerned in giving the backgrouds of some function spaces; the definitions of some holomorphic function spaces and Riemann-Stieltjes operators are given;some known results which are close to this thesis are also listed.Charpter 2 is aimed at investigating some new characterizations of the Bloch spaces and theα-Bloch spaces.Using the technique of pseuohyperbolic metric ball,we obtain the direvative-free characterization,single integral characterization, double integral characterization and mixture of derivative characterizations of the Bloch spaces.For theα-Bloch spaces,a derivative-free characterization(for anyα＞0),an integral characterization and a coefficient characterization are shown.Charpter 3 is concentrated at studing some new characterizations of the Besov spaces and the generalized weighted Bergman spaces.We obtain several derivatie-free characterizations,double integral characterizations,three integral characterizations and mixture characterizations of the Besov spaces and the generalized weighted Bergman spaces by using the technique of pseuohyperbolic metric ball.Charpter 4 is concerned in characterizations of the Dirichlet type spaces on the unit ball.Several derivatie-free characterizations,oscillation characterizations and mixture characterizations of the Dirichlet type spaces and the Q_p space are obtained.Chapter 5 is devoted to investigate the boundedness and compactness of the Riemann-Stieltjes integral operators on holomorphic function spaces.Some sufficient and necesary conditions for Riemann-Stieltjes operators on the Hardy spaces,the weighted Bergman spaces,the mixed norm spaces,theα-Bloch spaces and the Zygmund spaces to be bounded and compact are given.