Operators On Bergman Spaces Induced By Regular Weights

This paper is devoted to studying the operators on the regular weighted Bergman spaces in two types of regions.Firstly,we use the Berezin transform,some estimates about the reproducing kernels and the regular weights to char-acterize the boundedness and compactness of Toeplitz operator T?w between the different weighted Bergman spaces Avp and Avq on unit disk with 1<p,q<?,which is induced by w and the positive Borel measure ?.Secondly,we use the (?)—equation and some estimates about the reproducing kernels and the weights to describe the boundedness and compactness of Hankel operator Hf between the weighted Bergman space Aw1,2 p and Lebesgue spaceLw1,2 q,with 1<p,q<? on the annulus,which is induced by Lw1,2 l(M).In Chapter 1,we introduce the research background about Bergman spaces,Toeplitz operators and Hankel operators.Then we give the preliminary knowledge about the regular weighted Bergman spaces on the unit disc and on the annulus,and also show the main results in this paper.In Chapter 2,we give some estimates of reproducing kernels on the regular weighted Bergman spaces of the unit disk.Then we discuss the boundedness and compactness of the Topolitz operator in the case of 1<p?q?? and 1<q<p<?.In Chapter 3,we give some estimates of reproducing kernels and the solution of the (?)—equation on the regular weighted Bergman spaces of the annulus.Then we discuss the boundedness and compactness of Hankel operator in the case of 1<p?q?? and 1?q ?p??.Finally some applications of the main theorems are given.