Atomic Decomposition Of Békollé-bonami Weighted Bergman Spaces In The Unit Ball

On the unit ball in the n dimensional complex Euclidean space,we investigate the atomic decomposition of the weighted Bergman spaces with Békollé-Bonami weights.First of all,it focuses on the research background and current situation of Bergman space theory,weighted Bergman space theory,and the research background and significance of atomic decomposi-tion theory.In terms of research background,it describes the development process of these theories;for the research significance,it also extends to the connection between theory and each space.Bergman space theory has always been a hot topic in function theory,then the standard weighted Bergman space has been widely concerned,the problems involved such as atomic decomposition and interpolation have been studied by many mathematicians for a long time.Atomic decomposition theory is a very important tool in the study of function space and operator theory.In this paper,we first generalize the atomic decomposition theo-rem,then we use the atomic decomposition theorem to study the compact difference problem of composite operators.In chapter 3,we give the atomic decomposition theorem of this weighted Bergman space by using the reproducing kernel function of Békollé-Bonami weighted Bergman space,then we modify the Luecking's atomic decomposition theorem by the reproducing kernel functions of A2(u)of the weighted Bergman space.Then in chapter 4,we characterize the bounded difference of composition operators from the standard weighted Bergman space to the Lebesgue space when 0<q<p.Compared with the case of unweighted,the equivalent condition of compact difference and the com-pactness of weighted composite operator is proved by using the atomic decomposition the-orem of unweighted Bergman space,we generalize to the characterization of difference of composite operators in Békollé-Bonami weighted Bergman spaces.In this process,we find the interesting relationship between the difference operators and some weighted composition operators,the boundedness between standard weighted Bergman Spaces and the complete characterization of compact difference are obtained.A sufficient condition of the difference of composite operator is bounded and the necessary and sufficient condition for the bound-edness of weighted composite operators are given.Finally,the following research ideas and objectives are given by using the atomic decomposition theorem.