Weighted Carleson Measure Spaces Associated With Zygmund Dilations

In this dessertation,we introduce the weighted Carleson measure spaces associated with Zygmund dilations and prove that such spaces are well defined.We then develop a new theory for weighted Carleson measure spaces.This includes the study of density of the weighted Carleson measure spaces,duality between the weighted Carleson maesure spaces and weighted Hardy spaces,and the study of singular integral operators on such spaces,which,particularly,provides the weighted estimates for those singular integral operator introduced by Ricci-Stein and FeffermanPipher.All these results are new even under the unweighted setting.