Weighted Estimates For Commutators

Let T be the Calder′on-Zygmund singular integral operatorLet b be a locally integrable function on Rn, the commutator Tb generated by the functionb and the operator T is defined byfor suitable functions f.In this thesis, the author studies the weighted estimates of the classical singular integralcommutators , their corresponding endpoint estimates are also discussed. This thesisconsists three chapters.Chapter 1 presents the background and give out some necessary notations as well asdefinitions of spaces.In chapter 2, we consider the boundedness of the commutator Tb with the weightedBMO functions on weighted Hardy spaces, weighted Herz spaces and weighted Herz-typeHardy spaces provided forμ∈A1 and b∈BMOμ.In chapter 3, we consider the boundedness of the commutator Tb with the weightedLipschitz functions on weighted Hardy spaces, weighted Herz spaces and weighted Herz-type Hardy spaces provided forμ∈A1 and b∈Lipβ,μ.